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

analyze254.0ms (2.1%)

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 20 to 14 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 158.0ms

ival-pow: 50.0ms (31.6% of total)

ival-sin: 38.0ms (24.1% of total)

ival-sqrt: 32.0ms (20.3% of total)

ival-mult: 21.0ms (13.3% of total)

ival-add: 9.0ms (5.7% of total)

ival-div: 6.0ms (3.8% of total)

const: 2.0ms (1.3% of total)

backward-pass: 1.0ms (0.6% of total)

sample1.7s (13.6%)

Results

1.3s

8256×

valid

Precisions

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

ival-sin: 590.0ms (57.3% of total)

ival-pow: 194.0ms (18.9% of total)

ival-sqrt: 63.0ms (6.1% of total)

ival-mult: 60.0ms (5.8% of total)

ival-div: 55.0ms (5.3% of total)

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

const: 13.0ms (1.3% of total)

backward-pass: 3.0ms (0.3% of total)

Bogosity

preprocess127.0ms (1%)

Algorithm

2×	egg-herbie

Rules

2204×	`fnmadd-define`
1936×	`fma-define`
1234×	`sum3-define`
1150×	`fmsub-define`
1132×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	166
1	104	113
2	232	113
3	420	113
4	1025	113
5	2827	113
6	4704	113
7	6184	113
8	7067	113
9	7216	113
10	7327	113
11	7359	113
12	7359	113
0	13	16
1	19	11
2	27	11
3	28	11
0	28	11

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
(* (/ (sin ky) (sqrt (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))) (sin th))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
(* (/ (sin (neg ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))) (sin th))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (neg (sin th)))
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin (neg th)))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (neg (sin th)))
(neg (* (/ (sin ky) (sqrt (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))) (sin th)))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (neg (sin th)))
(neg (* (/ (sin (neg ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))) (sin th)))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
(neg (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin (neg th))))
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
(* (/ (sin kx) (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin th))
(/ (* (sin kx) (sin th)) (hypot (sin ky) (sin kx)))
(* (/ (sin ky) (sqrt (+ (pow (sin th) 2) (pow (sin ky) 2)))) (sin kx))
(/ (* (sin ky) (sin kx)) (hypot (sin ky) (sin th)))
(* (/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin th) 2)))) (sin ky))
(/ (* (sin ky) (sin th)) (hypot (sin kx) (sin th)))

Symmetry

(abs kx)

(negabs ky)

(negabs th)

explain168.0ms (1.4%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
19	0	-	3	(5.587227855350128e-301 1.457621110242678e-159 5.038602414192752e-193)	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	0	-	0	-	`kx`
0	0	-	0	-	`ky`
0	0	-	0	-	`(sin.f64 ky)`
0	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	-	0	-	`#s(literal 2 binary64)`
0	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	-	0	-	`th`
0	51	(1.662996069189453e-129 8.59458197249154e-65 2.0374028676816745e+52)	0	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	0	-	0	-	`(sin.f64 th)`
0	0	-	0	-	`(sin.f64 kx)`
0	0	-	0	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	72	(2.48991770591953e+52 7.677724671228982e-41 2.5390532334045585e-283)	0	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`

Results

101.0ms

512×

valid

Compiler

Compiled 159 to 41 computations (74.2% saved)

Precisions

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

ival-sin: 35.0ms (57.4% of total)

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

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

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

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

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

const: 1.0ms (1.6% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	92.9%	(*.f64 (/.f64 (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%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

Status

Accuracy

Program

▶

92.9%

(*.f64 (/.f64 (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%

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

Compiler

Compiled 33 to 22 computations (33.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	12992	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	cost-diff	12992	(/.f64 (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	12992	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	0	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

Rules

16×	`-lowering-.f32`
16×	`-lowering-.f64`
6×	`*-commutative`
6×	`sin-lowering-sin.f64`
6×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	84
1	29	84
2	33	84
0	33	84

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize111.0ms (0.9%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	accuracy	99.7%	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓	accuracy	99.6%	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
✓	accuracy	93.3%	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	accuracy	100.0%	(sin.f64 kx)
✓	accuracy	99.9%	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	accuracy	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	accuracy	99.6%	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Results

86.0ms

256×

valid

Compiler

Compiled 103 to 17 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-pow: 23.0ms (31.4% of total)

ival-sin: 17.0ms (23.2% of total)

compiled-spec: 10.0ms (13.7% of total)

ival-div: 7.0ms (9.6% of total)

ival-mult: 7.0ms (9.6% of total)

ival-add: 5.0ms (6.8% of total)

ival-sqrt: 4.0ms (5.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series39.0ms (0.3%)

Counts

11 → 240

Calls

Call 1

Inputs
#<alt (* (sin ky) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))>
#<alt (sin ky)>
#<alt (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))>
#<alt (sin th)>
#<alt (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))>
#<alt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))>
#<alt (sin kx)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin ky) 2)>

Outputs
#<alt (/ (* ky (sin th)) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* 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)))))))>
#<alt (* 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))))))))))>
#<alt (* 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))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin th)>
#<alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt ky>
#<alt (* ky (+ 1 (* -1/6 (pow ky 2))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* 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))))))))>
#<alt (* 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))))))))))>
#<alt (* 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)))))))))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ (sin th) (sin kx))>
#<alt (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))>
#<alt (+ (* (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)))>
#<alt (+ (* (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)))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ (sin th) (sin ky))>
#<alt (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))>
#<alt (+ (* (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)))>
#<alt (+ (* (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)))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt th>
#<alt (* th (+ 1 (* -1/6 (pow th 2))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (/ (* ky (sin th)) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin th)>
#<alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* 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)))))))>
#<alt (* 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))))))))))>
#<alt (* 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))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ ky (sin kx))>
#<alt (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))>
#<alt (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin ky)>
#<alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin kx)>
#<alt (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))>
#<alt (+ (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))))))>
#<alt (+ (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))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin kx)>
#<alt (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))>
#<alt (+ (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))))))>
#<alt (+ (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))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin ky)>
#<alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt kx>
#<alt (* kx (+ 1 (* -1/6 (pow kx 2))))>
#<alt (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))>
#<alt (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (pow kx 2)>
#<alt (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))>
#<alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))>
#<alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow ky 2)>
#<alt (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))>
#<alt (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))>
#<alt (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>

Calls

60 calls:

Time	Variable		Point	Expression
6.0ms	th	@	inf	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
3.0ms	ky	@	-inf	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
3.0ms	ky	@	inf	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
3.0ms	ky	@	0	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
2.0ms	kx	@	inf	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))

rewrite224.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1716×	`-lowering-.f32`
1716×	`-lowering-.f64`
1580×	`/-lowering-/.f32`
1580×	`/-lowering-/.f64`
1226×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	62
1	101	62
2	758	62
0	9823	62

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 284

Calls

Call 1

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

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

simplify277.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

5238×	`-lowering-.f32`
5238×	`-lowering-.f64`
1906×	`+-lowering-+.f64`
1906×	`+-lowering-+.f32`
1622×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	405	4445
1	1412	4111
2	5844	4111
0	8117	4111

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

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

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

eval109.0ms (0.9%)

Compiler: Compiled 14023 to 1585 computations (88.7% saved)

prune80.0ms (0.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	625	17	642
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	626	18	644

Accuracy

99.9%

Counts

644 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	33.9%	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
	79.4%	(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
▶	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
▶	44.3%	(*.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))))) th)
	38.1%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
	35.5%	(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
	23.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
	90.6%	(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
	28.3%	(.f64 (.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))) (sin.f64 th))
	42.3%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
	45.8%	(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) th) th))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	59.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) kx)))
▶	62.1%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
▶	30.2%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
	38.1%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
	46.6%	(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
▶	30.3%	(sin.f64 th)

Compiler

Compiled 524 to 361 computations (31.1% saved)

simplify395.0ms (3.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	12992	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	cost-diff	12992	(/.f64 (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	12992	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	0	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(/.f64 (sin.f64 th) (sin.f64 ky))
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	13056	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))

Rules

7772×	`-lowering-.f32`
7772×	`-lowering-.f64`
4376×	`associate-/r/`
3818×	`/-lowering-/.f32`
3818×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	127
1	45	127
2	59	127
3	65	127
4	68	127
5	70	127
6	144	127
7	409	127
8	1682	127
9	2239	127
10	2835	127
11	3172	127
12	3408	127
13	3804	127
14	4384	127
15	5165	127
16	5519	127
17	5691	127
18	5777	127
19	5841	127
20	5903	127
21	6695	127
22	7191	127
23	7291	127
24	7376	127
25	7452	127
0	10505	127

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize187.0ms (1.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 (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	99.7%	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓	accuracy	99.6%	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
✓	accuracy	93.3%	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	accuracy	100.0%	(sin.f64 ky)
✓	accuracy	100.0%	(sin.f64 kx)
✓	accuracy	99.7%	(/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))
✓	accuracy	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
✓	accuracy	100.0%	(sin.f64 th)
✓	accuracy	100.0%	(sin.f64 ky)
✓	accuracy	99.7%	(/.f64 (sin.f64 th) (sin.f64 ky))
✓	accuracy	99.7%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
✓	accuracy	100.0%	(sin.f64 th)
✓	accuracy	100.0%	(sin.f64 kx)
✓	accuracy	99.9%	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
✓	accuracy	99.8%	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	accuracy	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))

Results

146.0ms

256×

valid

Compiler

Compiled 152 to 22 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-sin: 17.0ms (21.4% of total)

compiled-spec: 17.0ms (21.4% of total)

ival-mult: 13.0ms (16.4% of total)

ival-pow: 13.0ms (16.4% of total)

ival-sqrt: 8.0ms (10.1% of total)

ival-div: 6.0ms (7.5% of total)

ival-add: 4.0ms (5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series35.0ms (0.3%)

Counts

15 → 348

Calls

Call 1

Inputs
#<alt (* (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th))>
#<alt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))>
#<alt (sin ky)>
#<alt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))>
#<alt (sin th)>
#<alt (* (sin ky) (/ (sin th) (sin ky)))>
#<alt (/ (sin th) (sin ky))>
#<alt (* (sin ky) (/ (sin th) (sqrt (+ (* ky ky) (* (sin kx) (sin kx))))))>
#<alt (/ (sin th) (sqrt (+ (* ky ky) (* (sin kx) (sin kx)))))>
#<alt (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) th)>
#<alt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin kx)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin ky) 2)>

Outputs
#<alt (/ (* ky (sin th)) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin th)>
#<alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* 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)))))))>
#<alt (* 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))))))))))>
#<alt (* 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))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ ky (sin kx))>
#<alt (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))>
#<alt (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt ky>
#<alt (* ky (+ 1 (* -1/6 (pow ky 2))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin kx)>
#<alt (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))>
#<alt (+ (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))))))>
#<alt (+ (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))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt th>
#<alt (* th (+ 1 (* -1/6 (pow th 2))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt th>
#<alt (* th (+ 1 (* -1/6 (pow th 2))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (/ th (sin ky))>
#<alt (* th (+ (* -1/6 (/ (pow th 2) (sin ky))) (/ 1 (sin ky))))>
#<alt (* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin ky))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))>
#<alt (* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin ky))) (* 1/120 (/ 1 (sin ky))))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) ky)>
#<alt (/ (+ (sin th) (* 1/6 (* (pow ky 2) (sin th)))) ky)>
#<alt (/ (+ (sin th) (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) ky)>
#<alt (/ (+ (sin th) (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 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))))) ky)>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (* ky (sin th)) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))>
#<alt (* 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))) (* 3/8 (/ (sin th) (pow (sin kx) 5))))))))) (/ (sin th) (sin kx))))>
#<alt (* 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))) (+ (* 3/8 (/ (sin th) (pow (sin kx) 5))) (* (pow ky 2) (+ (* -5/16 (/ (sin th) (pow (sin kx) 7))) (+ (* -1/16 (/ (sin th) (pow (sin kx) 5))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))>
#<alt (/ (* (sin ky) (sin th)) ky)>
#<alt (/ (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))) ky)>
#<alt (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th)))) ky)>
#<alt (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6)))) (pow ky 6))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))))) ky)>
#<alt (* -1 (/ (* (sin ky) (sin th)) ky))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))) ky))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th)))) ky))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6)))) (pow ky 6))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))))) ky))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))))>
#<alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))>
#<alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (/ (* (sin ky) (sin th)) ky)>
#<alt (+ (* -1/2 (/ (* (pow kx 2) (* (sin ky) (sin th))) (pow ky 3))) (/ (* (sin ky) (sin th)) ky))>
#<alt (+ (* (pow kx 2) (+ (* -1/2 (/ (* (sin ky) (sin th)) (pow ky 3))) (* 1/2 (* (pow kx 2) (* ky (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6))))))))))) (/ (* (sin ky) (sin th)) ky))>
#<alt (+ (* (pow kx 2) (+ (* -1/2 (/ (* (sin ky) (sin th)) (pow ky 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* ky (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))) (pow ky 2))) (+ (* 2/45 (/ 1 (pow ky 4))) (+ (* 2/3 (/ 1 (pow ky 6))) (/ 1 (pow ky 8)))))))))) (* 1/2 (* ky (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))))))))))) (/ (* (sin ky) (sin th)) ky))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* th (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))>
#<alt (* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))>
#<alt (* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))))))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (/ (sin th) (sin kx))>
#<alt (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))>
#<alt (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 3/8 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 5))))) (/ (sin th) (sin kx)))>
#<alt (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -5/16 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 7))) (* 3/8 (/ (sin th) (pow (sin kx) 5))))))) (/ (sin th) (sin kx)))>
#<alt (/ (sin th) ky)>
#<alt (/ (+ (sin th) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))) ky)>
#<alt (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2))))) ky)>
#<alt (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (+ (* -1/2 (/ (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6))) (pow ky 6))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))))) ky)>
#<alt (* -1 (/ (sin th) ky))>
#<alt (* -1 (/ (+ (sin th) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))) ky))>
#<alt (* -1 (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2))))) ky))>
#<alt (* -1 (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (+ (* -1/2 (/ (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6))) (pow ky 6))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))))) ky))>
#<alt (/ (sin th) ky)>
#<alt (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow ky 3))) (/ (sin th) ky))>
#<alt (+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow ky 3))) (* 1/2 (* (pow kx 2) (* ky (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))))))))) (/ (sin th) ky))>
#<alt (+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow ky 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* ky (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))) (pow ky 2))) (+ (* 2/45 (/ 1 (pow ky 4))) (+ (* 2/3 (/ 1 (pow ky 6))) (/ 1 (pow ky 8))))))))) (* 1/2 (* ky (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6))))))))))) (/ (sin th) ky))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))>
#<alt (/ (* ky th) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt th>
#<alt (+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))>
#<alt (+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))>
#<alt (+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ ky (sin kx))>
#<alt (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))>
#<alt (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin ky)>
#<alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin kx)>
#<alt (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))>
#<alt (+ (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))))))>
#<alt (+ (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))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt kx>
#<alt (* kx (+ 1 (* -1/6 (pow kx 2))))>
#<alt (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))>
#<alt (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (pow kx 2)>
#<alt (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))>
#<alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))>
#<alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow (sin kx) 2)>
#<alt (pow ky 2)>
#<alt (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))>
#<alt (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))>
#<alt (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin ky) 2)>

Calls

87 calls:

Time	Variable		Point	Expression
6.0ms	th	@	-inf	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) th)
3.0ms	th	@	0	(* (sin ky) (/ (sin th) (sqrt (+ (* ky ky) (* (sin kx) (sin kx))))))
1.0ms	kx	@	0	(* (sin ky) (/ (sin th) (sqrt (+ (* ky ky) (* (sin kx) (sin kx))))))
1.0ms	ky	@	-inf	(* (sin ky) (/ (sin th) (sqrt (+ (* ky ky) (* (sin kx) (sin kx))))))
1.0ms	kx	@	inf	(* (sin ky) (/ (sin th) (sqrt (+ (* ky ky) (* (sin kx) (sin kx))))))

rewrite262.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2560×	`-lowering-.f32`
2560×	`-lowering-.f64`
2410×	`/-lowering-/.f32`
2410×	`/-lowering-/.f64`
1328×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	85
1	130	85
2	896	85
0	9428	85

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 391

Calls

Call 1

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

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

simplify480.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

8974×	`-lowering-.f32`
8974×	`-lowering-.f64`
4432×	`+-lowering-+.f64`
4432×	`+-lowering-+.f32`
1764×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	660	6231
1	2346	5822
0	9038	5822

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(/ th (sin ky))
(* th (+ (* -1/6 (/ (pow th 2) (sin ky))) (/ 1 (sin ky))))
(* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin ky))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))
(* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin ky))) (* 1/120 (/ 1 (sin ky))))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) ky)
(/ (+ (sin th) (* 1/6 (* (pow ky 2) (sin th)))) ky)
(/ (+ (sin th) (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) ky)
(/ (+ (sin th) (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 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))))) ky)
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (sin th) (sin ky))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 3/8 (/ (sin th) (pow (sin kx) 5))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 3/8 (/ (sin th) (pow (sin kx) 5))) (* (pow ky 2) (+ (* -5/16 (/ (sin th) (pow (sin kx) 7))) (+ (* -1/16 (/ (sin th) (pow (sin kx) 5))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* (sin ky) (sin th)) ky)
(/ (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))) ky)
(/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th)))) ky)
(/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6)))) (pow ky 6))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))))) ky)
(* -1 (/ (* (sin ky) (sin th)) ky))
(* -1 (/ (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))) ky))
(* -1 (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th)))) ky))
(* -1 (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6)))) (pow ky 6))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))))) ky))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(/ (* (sin ky) (sin th)) ky)
(+ (* -1/2 (/ (* (pow kx 2) (* (sin ky) (sin th))) (pow ky 3))) (/ (* (sin ky) (sin th)) ky))
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (sin ky) (sin th)) (pow ky 3))) (* 1/2 (* (pow kx 2) (* ky (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6))))))))))) (/ (* (sin ky) (sin th)) ky))
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (sin ky) (sin th)) (pow ky 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* ky (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))) (pow ky 2))) (+ (* 2/45 (/ 1 (pow ky 4))) (+ (* 2/3 (/ 1 (pow ky 6))) (/ 1 (pow ky 8)))))))))) (* 1/2 (* ky (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))))))))))) (/ (* (sin ky) (sin th)) ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* th (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(/ (sin th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 3/8 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 5))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -5/16 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 7))) (* 3/8 (/ (sin th) (pow (sin kx) 5))))))) (/ (sin th) (sin kx)))
(/ (sin th) ky)
(/ (+ (sin th) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))) ky)
(/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2))))) ky)
(/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (+ (* -1/2 (/ (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6))) (pow ky 6))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))))) ky)
(* -1 (/ (sin th) ky))
(* -1 (/ (+ (sin th) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))) ky))
(* -1 (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2))))) ky))
(* -1 (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (+ (* -1/2 (/ (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6))) (pow ky 6))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))))) ky))
(/ (sin th) ky)
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow ky 3))) (/ (sin th) ky))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow ky 3))) (* 1/2 (* (pow kx 2) (* ky (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))))))))) (/ (sin th) ky))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow ky 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* ky (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))) (pow ky 2))) (+ (* 2/45 (/ 1 (pow ky 4))) (+ (* 2/3 (/ 1 (pow ky 6))) (/ 1 (pow ky 8))))))))) (* 1/2 (* ky (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6))))))))))) (/ (sin th) ky))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(/ (* ky th) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)

Outputs
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal 1/2 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))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64)))) (.f64 ky (.f64 ky (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 th) (.f64 (sin.f64 kx) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))))))) (+.f64 (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/5040 binary64)) (sin.f64 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+.f64 (sin.f64 th) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 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)))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 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))))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(.f64 th (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (*.f64 th th)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 th (+.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (.f64 (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 (.f64 #s(literal 1/120 binary64) (*.f64 th th)) (sin.f64 ky)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(.f64 th (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 th th)) (sin.f64 ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 #s(literal -1/5040 binary64) (.f64 th th)) (sin.f64 ky)) (.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (.f64 (.f64 th th) (.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (.f64 ky (-.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 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))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 (.f64 ky ky) (+.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)))) (.f64 ky (.f64 ky (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 kx) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))))) (-.f64 (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx))) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (.f64 kx kx)))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(+ 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))))))
(+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx (.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal -1/6 binary64))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 ky (.f64 ky (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 ky ky) #s(literal -1/5040 binary64))))) #s(literal -1/6 binary64)))))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+.f64 (sin.f64 ky) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (sin.f64 ky)))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+.f64 (sin.f64 ky) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx (*.f64 kx (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(+.f64 (sin.f64 ky) (.f64 (.f64 kx kx) (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (.f64 (.f64 kx kx) (+.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (+.f64 #s(literal 2/45 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 ky)))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+.f64 (sin.f64 kx) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (sin.f64 kx)))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+.f64 (sin.f64 kx) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 ky ky)) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(+.f64 (sin.f64 kx) (.f64 (.f64 ky ky) (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 kx)) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (+.f64 #s(literal 2/45 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (sin.f64 kx)))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 th th) (+.f64 (.f64 #s(literal 1/120 binary64) (*.f64 th th)) #s(literal -1/6 binary64)))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 th th) (+.f64 (.f64 th (.f64 th (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 th th))))) #s(literal -1/6 binary64)))))
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 th th) (+.f64 (.f64 #s(literal 1/120 binary64) (*.f64 th th)) #s(literal -1/6 binary64)))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 th th) (+.f64 (.f64 th (.f64 th (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 th th))))) #s(literal -1/6 binary64)))))
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(/ th (sin ky))
(/.f64 th (sin.f64 ky))
(* th (+ (* -1/6 (/ (pow th 2) (sin ky))) (/ 1 (sin ky))))
(.f64 th (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (.f64 th (*.f64 th #s(literal -1/6 binary64))) (sin.f64 ky))))
(* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin ky))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))
(.f64 th (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 th (.f64 th (+.f64 (/.f64 (.f64 #s(literal 1/120 binary64) (*.f64 th th)) (sin.f64 ky)) (/.f64 #s(literal -1/6 binary64) (sin.f64 ky)))))))
(* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin ky))) (* 1/120 (/ 1 (sin ky))))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))
(.f64 th (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (.f64 th th) (+.f64 (.f64 (.f64 th th) (+.f64 (/.f64 (.f64 #s(literal -1/5040 binary64) (*.f64 th th)) (sin.f64 ky)) (/.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (/.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) ky)
(/.f64 (sin.f64 th) ky)
(/ (+ (sin th) (* 1/6 (* (pow ky 2) (sin th)))) ky)
(/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (*.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky)
(/ (+ (sin th) (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) ky)
(/.f64 (+.f64 (sin.f64 th) (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 ky ky) (.f64 (sin.f64 th) #s(literal 7/360 binary64))) (.f64 (sin.f64 th) #s(literal 1/6 binary64))))) ky)
(/ (+ (sin th) (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 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))))) ky)
(/.f64 (+.f64 (sin.f64 th) (.f64 ky (.f64 ky (+.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (.f64 (sin.f64 th) #s(literal 1/840 binary64)) (.f64 (sin.f64 th) #s(literal -7/2160 binary64))) (.f64 #s(literal -1 binary64) (.f64 ky ky))) (.f64 (sin.f64 th) #s(literal 7/360 binary64)))) (*.f64 (sin.f64 th) #s(literal 1/6 binary64)))))) ky)
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 3/8 (/ (sin th) (pow (sin kx) 5))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 3/8 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 5 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))) (+ (* 3/8 (/ (sin th) (pow (sin kx) 5))) (* (pow ky 2) (+ (* -5/16 (/ (sin th) (pow (sin kx) 7))) (+ (* -1/16 (/ (sin th) (pow (sin kx) 5))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky (.f64 ky (+.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 3/8 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 5 binary64))))) (.f64 (.f64 ky ky) (+.f64 (+.f64 (/.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/5040 binary64)) (sin.f64 kx))) (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 5 binary64))) (/.f64 (.f64 #s(literal -5/16 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 7 binary64)))))))))))))
(/ (* (sin ky) (sin th)) ky)
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(/ (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))) ky)
(/.f64 (+.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (.f64 (sin.f64 th) (sin.f64 ky))) (*.f64 ky ky))) ky)
(/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th)))) ky)
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(/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6)))) (pow ky 6))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))))) ky)
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(* -1 (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th)))) ky))
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(* -1 (/ (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow ky 4))) (+ (* -1/2 (/ (* (sin ky) (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6)))) (pow ky 6))) (+ (* -1/2 (/ (* (pow (sin kx) 2) (* (sin ky) (sin th))) (pow ky 2))) (* (sin ky) (sin th))))) ky))
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(* (* th (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(/ (* (sin ky) (sin th)) ky)
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
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(+ (* (pow kx 2) (+ (* -1/2 (/ (* (sin ky) (sin th)) (pow ky 3))) (* 1/2 (* (pow kx 2) (* ky (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6))))))))))) (/ (* (sin ky) (sin th)) ky))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* th (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))
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(* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))))))))
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(* th (+ (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))))))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
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(/ (sin th) (sin kx))
(/.f64 (sin.f64 th) (sin.f64 kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
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(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -5/16 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 7))) (* 3/8 (/ (sin th) (pow (sin kx) 5))))))) (/ (sin th) (sin kx)))
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(/ (sin th) ky)
(/.f64 (sin.f64 th) ky)
(/ (+ (sin th) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))) ky)
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(/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2))))) ky)
(/.f64 (+.f64 (sin.f64 th) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 (sin.f64 th) (.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal -3/4 binary64))) (pow.f64 ky #s(literal 4 binary64))) (/.f64 (.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (*.f64 ky ky))))) ky)
(/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (+ (* -1/2 (/ (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6))) (pow ky 6))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))))) ky)
(/.f64 (+.f64 (sin.f64 th) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 (sin.f64 th) (.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal -3/4 binary64))) (pow.f64 ky #s(literal 4 binary64))) (+.f64 (/.f64 (.f64 (sin.f64 th) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal -3/4 binary64)) #s(literal 1/2 binary64))))) (pow.f64 ky #s(literal 6 binary64))) (/.f64 (.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (*.f64 ky ky)))))) ky)
(* -1 (/ (sin th) ky))
(-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 th) ky))
(* -1 (/ (+ (sin th) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))) ky))
(/.f64 (+.f64 (sin.f64 th) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (*.f64 ky ky))) (neg.f64 ky))
(* -1 (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2))))) ky))
(/.f64 (+.f64 (sin.f64 th) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 (sin.f64 th) (.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal -3/4 binary64))) (pow.f64 ky #s(literal 4 binary64))) (/.f64 (.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (*.f64 ky ky))))) (neg.f64 ky))
(* -1 (/ (+ (sin th) (+ (* -1/2 (/ (* (sin th) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4)))) (pow ky 4))) (+ (* -1/2 (/ (* (sin th) (+ (* 1/2 (* (pow (sin kx) 2) (+ (* -1 (pow (sin kx) 4)) (* 1/4 (pow (sin kx) 4))))) (pow (sin kx) 6))) (pow ky 6))) (* -1/2 (/ (* (pow (sin kx) 2) (sin th)) (pow ky 2)))))) ky))
(/.f64 (+.f64 (sin.f64 th) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 (sin.f64 th) (.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal -3/4 binary64))) (pow.f64 ky #s(literal 4 binary64))) (+.f64 (/.f64 (.f64 (sin.f64 th) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal -3/4 binary64)) #s(literal 1/2 binary64))))) (pow.f64 ky #s(literal 6 binary64))) (/.f64 (.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (*.f64 ky ky)))))) (neg.f64 ky))
(/ (sin th) ky)
(/.f64 (sin.f64 th) ky)
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow ky 3))) (/ (sin th) ky))
(+.f64 (/.f64 (sin.f64 th) ky) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (/.f64 (sin.f64 th) (.f64 ky (*.f64 ky ky)))))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow ky 3))) (* 1/2 (* (pow kx 2) (* ky (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))))))))) (/ (sin th) ky))
(+.f64 (/.f64 (sin.f64 th) ky) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (.f64 ky (.f64 ky ky))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 ky (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 ky #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 ky #s(literal 6 binary64))))))))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow ky 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* ky (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6)))) (pow ky 2))) (+ (* 2/45 (/ 1 (pow ky 4))) (+ (* 2/3 (/ 1 (pow ky 6))) (/ 1 (pow ky 8))))))))) (* 1/2 (* ky (* (sin th) (+ (* 1/3 (/ 1 (pow ky 4))) (* 3/4 (/ 1 (pow ky 6))))))))))) (/ (sin th) ky))
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(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ (pow ky 2) (pow (sin kx) 2)))))
(.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/ (* ky th) (sin kx))
(*.f64 ky (/.f64 th (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))
(.f64 ky (+.f64 (/.f64 th (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (*.f64 #s(literal -1/6 binary64) (/.f64 th (sin.f64 kx)))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
(.f64 ky (+.f64 (/.f64 th (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal -1/6 binary64) (/.f64 th (sin.f64 kx))) (.f64 (.f64 ky ky) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) th))) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 #s(literal 1/120 binary64) (/.f64 th (sin.f64 kx)))))))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
(.f64 ky (+.f64 (/.f64 th (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (.f64 #s(literal -1/6 binary64) (/.f64 th (sin.f64 kx))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 ky (.f64 ky (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) th)))) (+.f64 (.f64 ky (.f64 ky (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (sin.f64 kx))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))))) (+.f64 (.f64 th (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/240 binary64) th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 #s(literal -1/5040 binary64) (/.f64 th (sin.f64 kx)))))))) (*.f64 #s(literal 1/120 binary64) (/.f64 th (sin.f64 kx)))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+.f64 th (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 kx kx) (.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(+.f64 th (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (.f64 ky (-.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 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))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 (.f64 ky ky) (+.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)))) (.f64 ky (.f64 ky (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 kx) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))))) (-.f64 (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx))) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (.f64 kx kx)))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(+ 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))))))
(+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx (.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+.f64 (sin.f64 ky) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (sin.f64 ky)))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+.f64 (sin.f64 ky) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx (*.f64 kx (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(+.f64 (sin.f64 ky) (.f64 (.f64 kx kx) (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (.f64 (.f64 kx kx) (+.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (+.f64 #s(literal 2/45 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 ky)))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+.f64 (sin.f64 kx) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (sin.f64 kx)))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+.f64 (sin.f64 kx) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 ky ky)) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(+.f64 (sin.f64 kx) (.f64 (.f64 ky ky) (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 kx)) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (+.f64 #s(literal 2/45 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (sin.f64 kx)))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(.f64 kx (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 kx kx))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(.f64 kx (+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 #s(literal 1/120 binary64) (*.f64 kx kx)) #s(literal -1/6 binary64))))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(.f64 kx (+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 (.f64 kx kx) (+.f64 #s(literal 1/120 binary64) (.f64 #s(literal -1/5040 binary64) (*.f64 kx kx)))) #s(literal -1/6 binary64))))))
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) #s(literal -1/3 binary64))) kx) kx)
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(.f64 (.f64 kx kx) (+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal -1/3 binary64))))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(.f64 (.f64 kx kx) (+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (+.f64 (.f64 kx (.f64 kx (+.f64 #s(literal 2/45 binary64) (.f64 (.f64 kx kx) #s(literal -1/315 binary64))))) #s(literal -1/3 binary64)))))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(.f64 ky (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/3 binary64)))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(.f64 ky (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64))))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(.f64 (.f64 ky ky) (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 ky ky) (+.f64 #s(literal 2/45 binary64) (.f64 (.f64 ky ky) #s(literal -1/315 binary64)))) #s(literal -1/3 binary64)))))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))

eval131.0ms (1.1%)

Compiler: Compiled 20393 to 2333 computations (88.6% saved)

prune184.0ms (1.5%)

Pruning

52 alts after pruning (48 fresh and 4 done)

	Pruned	Kept	Total
New	1060	38	1098
Fresh	2	10	12
Picked	2	3	5
Done	0	1	1
Total	1064	52	1116

Accuracy

99.9%

Counts

1116 → 52

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	12.8%	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	36.0%	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
	33.9%	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
	30.2%	(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
	11.9%	(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
	79.4%	(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
▶	99.5%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
▶	99.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))) (sin.f64 th))
	99.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th))))
	99.4%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
	79.4%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))))
	96.3%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th)))))
	45.9%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))))
✓	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
	46.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
	62.1%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
	60.0%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 kx (sin.f64 ky))) (sin.f64 th))
✓	44.3%	(*.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))))) th)
	27.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 ky (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64))))))))) th)
	38.1%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
	18.9%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
	35.5%	(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
	17.6%	(*.f64 (/.f64 ky (sin.f64 kx)) th)
	62.0%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	35.9%	(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
	23.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
	90.6%	(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
	53.2%	(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
	28.3%	(.f64 (.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))) (sin.f64 th))
	60.7%	(.f64 (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	42.3%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
	60.1%	(.f64 (sin.f64 ky) (/.f64 (.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (sin.f64 ky)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 th)))) (hypot.f64 ky (sin.f64 kx))))
	60.6%	(.f64 (sin.f64 ky) (/.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))) (hypot.f64 ky (sin.f64 kx))))
	20.8%	(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
	28.7%	(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))) (hypot.f64 ky (sin.f64 kx))))
✓	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	30.2%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	38.1%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
	20.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
	46.6%	(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	29.7%	(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
	30.1%	(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
▶	6.1%	(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
	28.4%	(*.f64 (exp.f64 (log.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (sin.f64 ky)))
	14.6%	(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
	70.3%	(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	20.7%	(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
	17.5%	(*.f64 ky (/.f64 th (sin.f64 kx)))
✓	30.3%	(sin.f64 th)
▶	15.0%	th

Compiler

Compiled 1571 to 1052 computations (33% saved)

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	cost-diff	256	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
✓	cost-diff	0	(cos.f64 (-.f64 ky th))
✓	cost-diff	0	(-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th)))
✓	cost-diff	128	(*.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64))
✓	cost-diff	128	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(/.f64 (sin.f64 th) (sin.f64 ky))
✓	cost-diff	0	(sin.f64 kx)
✓	cost-diff	0	(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	cost-diff	256	(hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
✓	cost-diff	256	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
✓	cost-diff	256	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))) (sin.f64 th))

Rules

2008×	`sum3-define`
1784×	`fnmadd-define`
1688×	`fma-define`
1138×	`-lowering-.f32`
1138×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	157
1	72	157
2	154	157
3	307	157
4	581	157
5	1019	157
6	1551	157
7	2342	157
8	4331	157
9	6178	157
10	7630	157
0	8146	157

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize390.0ms (3.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
✓	accuracy	99.8%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	accuracy	99.7%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	accuracy	89.0%	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
✓	accuracy	80.3%	(cos.f64 (+.f64 ky th))
✓	accuracy	80.0%	(cos.f64 (-.f64 ky th))
✓	accuracy	37.7%	(-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th)))
✓	accuracy	100.0%	(sin.f64 ky)
✓	accuracy	100.0%	(sin.f64 kx)
✓	accuracy	99.7%	(/.f64 (sin.f64 th) (sin.f64 ky))
✓	accuracy	99.6%	(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
✓	accuracy	99.8%	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
✓	accuracy	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))) (sin.f64 th))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))

Results

155.0ms	111×	2	valid
144.0ms	141×	1	valid
1.0ms	3×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 195 to 27 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 240.0ms

ival-sin: 46.0ms (19.2% of total)

ival-mult: 44.0ms (18.4% of total)

ival-cos: 37.0ms (15.4% of total)

compiled-spec: 34.0ms (14.2% of total)

backward-pass: 32.0ms (13.3% of total)

ival-div: 23.0ms (9.6% of total)

ival-add: 8.0ms (3.3% of total)

ival-sqrt: 8.0ms (3.3% of total)

ival-sub: 7.0ms (2.9% of total)

const: 1.0ms (0.4% of total)

series23.0ms (0.2%)

Counts

17 → 384

Calls

Call 1

Inputs
#<alt (* (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (/ 1 (/ 1 (sin ky))) (/ 1 (/ 1 (sin ky))))))) (sin th))>
#<alt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (/ 1 (/ 1 (sin ky))) (/ 1 (/ 1 (sin ky)))))))>
#<alt (sqrt (+ (* (sin kx) (sin kx)) (* (/ 1 (/ 1 (sin ky))) (/ 1 (/ 1 (sin ky))))))>
#<alt (/ 1 (/ 1 (sin ky)))>
#<alt (* (sin kx) (/ (sin th) (sin ky)))>
#<alt (sin kx)>
#<alt (/ (sin th) (sin ky))>
#<alt (sin th)>
#<alt (/ (* (- (cos (- ky th)) (cos (+ ky th))) 1) (* 2 (sin ky)))>
#<alt (* (- (cos (- ky th)) (cos (+ ky th))) 1)>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (cos (- ky th))>
#<alt (* (/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th))>
#<alt (/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))>
#<alt (/ 1 (sin ky))>
#<alt (sin ky)>
#<alt (cos (+ ky th))>

Outputs
#<alt (/ (* ky (sin th)) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin th)>
#<alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* 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)))))))>
#<alt (* 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))))))))))>
#<alt (* 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))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ ky (sin kx))>
#<alt (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))>
#<alt (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin ky)>
#<alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sin kx)>
#<alt (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))>
#<alt (+ (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))))))>
#<alt (+ (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))))))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt ky>
#<alt (* ky (+ 1 (* -1/6 (pow ky 2))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (/ (* kx (sin th)) (sin ky))>
#<alt (* kx (+ (* -1/6 (/ (* (pow kx 2) (sin th)) (sin ky))) (/ (sin th) (sin ky))))>
#<alt (* kx (+ (* (pow kx 2) (+ (* -1/6 (/ (sin th) (sin ky))) (* 1/120 (/ (* (pow kx 2) (sin th)) (sin ky))))) (/ (sin th) (sin ky))))>
#<alt (* kx (+ (* (pow kx 2) (+ (* -1/6 (/ (sin th) (sin ky))) (* (pow kx 2) (+ (* -1/5040 (/ (* (pow kx 2) (sin th)) (sin ky))) (* 1/120 (/ (sin th) (sin ky))))))) (/ (sin th) (sin ky))))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* th (sin kx)) (sin ky))>
#<alt (* th (+ (* -1/6 (/ (* (pow th 2) (sin kx)) (sin ky))) (/ (sin kx) (sin ky))))>
#<alt (* th (+ (* (pow th 2) (+ (* -1/6 (/ (sin kx) (sin ky))) (* 1/120 (/ (* (pow th 2) (sin kx)) (sin ky))))) (/ (sin kx) (sin ky))))>
#<alt (* th (+ (* (pow th 2) (+ (* -1/6 (/ (sin kx) (sin ky))) (* (pow th 2) (+ (* -1/5040 (/ (* (pow th 2) (sin kx)) (sin ky))) (* 1/120 (/ (sin kx) (sin ky))))))) (/ (sin kx) (sin ky))))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) ky)>
#<alt (/ (+ (* 1/6 (* (pow ky 2) (* (sin kx) (sin th)))) (* (sin kx) (sin th))) ky)>
#<alt (/ (+ (* (sin kx) (sin th)) (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 (* (sin kx) (sin th))) (* 1/120 (* (sin kx) (sin th)))))) (* -1/6 (* (sin kx) (sin th)))))) ky)>
#<alt (/ (+ (* (sin kx) (sin th)) (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/5040 (* (sin kx) (sin th))) (+ (* 1/720 (* (sin kx) (sin th))) (* 1/6 (+ (* -1/36 (* (sin kx) (sin th))) (* 1/120 (* (sin kx) (sin th))))))))) (+ (* -1/36 (* (sin kx) (sin th))) (* 1/120 (* (sin kx) (sin th)))))) (* -1/6 (* (sin kx) (sin th)))))) ky)>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt (/ (* (sin kx) (sin th)) (sin ky))>
#<alt kx>
#<alt (* kx (+ 1 (* -1/6 (pow kx 2))))>
#<alt (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))>
#<alt (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (sin kx)>
#<alt (/ th (sin ky))>
#<alt (* th (+ (* -1/6 (/ (pow th 2) (sin ky))) (/ 1 (sin ky))))>
#<alt (* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin ky))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))>
#<alt (* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin ky))) (* 1/120 (/ 1 (sin ky))))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) ky)>
#<alt (/ (+ (sin th) (* 1/6 (* (pow ky 2) (sin th)))) ky)>
#<alt (/ (+ (sin th) (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) ky)>
#<alt (/ (+ (sin th) (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 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))))) ky)>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt (/ (sin th) (sin ky))>
#<alt th>
#<alt (* th (+ 1 (* -1/6 (pow th 2))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))>
#<alt (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (sin th)>
#<alt (* 1/2 (/ (- (cos (neg th)) (cos th)) ky))>
#<alt (/ (+ (* 1/2 (* ky (- (sin th) (sin (neg th))))) (* 1/2 (- (cos (neg th)) (cos th)))) ky)>
#<alt (/ (+ (* 1/2 (- (cos (neg th)) (cos th))) (* ky (+ (* 1/2 (* ky (- (* -1/2 (cos (neg th))) (+ (* -1/2 (cos th)) (* -1/6 (- (cos (neg th)) (cos th))))))) (* 1/2 (- (sin th) (sin (neg th))))))) ky)>
#<alt (/ (+ (* 1/2 (- (cos (neg th)) (cos th))) (* ky (+ (* 1/2 (- (sin th) (sin (neg th)))) (* ky (+ (* 1/2 (* ky (- (* -1/6 (sin th)) (+ (* -1/6 (sin (neg th))) (* -1/6 (- (sin th) (sin (neg th)))))))) (* 1/2 (- (* -1/2 (cos (neg th))) (+ (* -1/2 (cos th)) (* -1/6 (- (cos (neg th)) (cos th))))))))))) ky)>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky)))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky)))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky)))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky)))) (sin ky)))>
#<alt (* 1/2 (/ (* th (- (sin ky) (* -1 (sin ky)))) (sin ky)))>
#<alt (* th (+ (* -1/6 (pow th 2)) (* 1/2 (/ (- (sin ky) (* -1 (sin ky))) (sin ky)))))>
#<alt (* th (+ (* 1/2 (/ (- (sin ky) (* -1 (sin ky))) (sin ky))) (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))>
#<alt (* th (+ (* 1/2 (/ (- (sin ky) (* -1 (sin ky))) (sin ky))) (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (- ky th)) (cos (+ ky th))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th)))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th)))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th)))) (sin ky)))>
#<alt (* 1/2 (/ (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th)))) (sin ky)))>
#<alt (- (cos (neg th)) (cos th))>
#<alt (- (+ (cos (neg th)) (* ky (- (sin th) (sin (neg th))))) (cos th))>
#<alt (- (+ (cos (neg th)) (* ky (- (+ (sin th) (* ky (- (* -1/2 (cos (neg th))) (* -1/2 (cos th))))) (sin (neg th))))) (cos th))>
#<alt (- (+ (cos (neg th)) (* ky (- (+ (sin th) (* ky (- (+ (* -1/2 (cos (neg th))) (* ky (- (* -1/6 (sin th)) (* -1/6 (sin (neg th)))))) (* -1/2 (cos th))))) (sin (neg th))))) (cos th))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (* th (- (sin ky) (* -1 (sin ky))))>
#<alt (* th (- (+ (sin ky) (* (pow th 2) (- (* -1/6 (sin ky)) (* 1/6 (sin ky))))) (* -1 (sin ky))))>
#<alt (* th (- (+ (sin ky) (* (pow th 2) (- (+ (* -1/6 (sin ky)) (* (pow th 2) (- (* 1/120 (sin ky)) (* -1/120 (sin ky))))) (* 1/6 (sin ky))))) (* -1 (sin ky))))>
#<alt (* th (- (+ (sin ky) (* (pow th 2) (- (+ (* -1/6 (sin ky)) (* (pow th 2) (- (+ (* 1/120 (sin ky)) (* (pow th 2) (- (* -1/5040 (sin ky)) (* 1/5040 (sin ky))))) (* -1/120 (sin ky))))) (* 1/6 (sin ky))))) (* -1 (sin ky))))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (neg th)) (cos th))>
#<alt (- (+ (cos (neg th)) (* ky (- (sin th) (sin (neg th))))) (cos th))>
#<alt (- (+ (cos (neg th)) (* ky (- (+ (sin th) (* ky (- (* -1/2 (cos (neg th))) (* -1/2 (cos th))))) (sin (neg th))))) (cos th))>
#<alt (- (+ (cos (neg th)) (* ky (- (+ (sin th) (* ky (- (+ (* -1/2 (cos (neg th))) (* ky (- (* -1/6 (sin th)) (* -1/6 (sin (neg th)))))) (* -1/2 (cos th))))) (sin (neg th))))) (cos th))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))>
#<alt (* th (- (sin ky) (* -1 (sin ky))))>
#<alt (* th (- (+ (sin ky) (* (pow th 2) (- (* -1/6 (sin ky)) (* 1/6 (sin ky))))) (* -1 (sin ky))))>
#<alt (* th (- (+ (sin ky) (* (pow th 2) (- (+ (* -1/6 (sin ky)) (* (pow th 2) (- (* 1/120 (sin ky)) (* -1/120 (sin ky))))) (* 1/6 (sin ky))))) (* -1 (sin ky))))>
#<alt (* th (- (+ (sin ky) (* (pow th 2) (- (+ (* -1/6 (sin ky)) (* (pow th 2) (- (+ (* 1/120 (sin ky)) (* (pow th 2) (- (* -1/5040 (sin ky)) (* 1/5040 (sin ky))))) (* -1/120 (sin ky))))) (* 1/6 (sin ky))))) (* -1 (sin ky))))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (- ky th)) (cos (+ ky th)))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))>
#<alt (cos (neg th))>
#<alt (+ (cos (neg th)) (* -1 (* ky (sin (neg th)))))>
#<alt (+ (cos (neg th)) (* ky (- (* -1/2 (* ky (cos (neg th)))) (sin (neg th)))))>
#<alt (+ (cos (neg th)) (* ky (- (* ky (+ (* -1/2 (cos (neg th))) (* 1/6 (* ky (sin (neg th)))))) (sin (neg th)))))>
#<alt (cos (- ky th))>
#<alt (cos (- ky th))>
#<alt (cos (- ky th))>
#<alt (cos (- ky th))>
#<alt (cos (neg (+ th (* -1 ky))))>
#<alt (cos (neg (+ th (* -1 ky))))>
#<alt (cos (neg (+ th (* -1 ky))))>
#<alt (cos (neg (+ th (* -1 ky))))>
#<alt (cos ky)>
#<alt (+ (cos ky) (* th (sin ky)))>
#<alt (+ (cos ky) (* th (- (* -1/2 (* th (cos ky))) (* -1 (sin ky)))))>
#<alt (+ (cos ky) (* th (- (* th (+ (* -1/2 (cos ky)) (* -1/6 (* th (sin ky))))) (* -1 (sin ky)))))>
#<alt (cos (- ky th))>
#<alt (cos (- ky th))>
#<alt (cos (- ky th))>
#<alt (cos (- ky th))>
#<alt (cos (+ ky (* -1 th)))>
#<alt (cos (+ ky (* -1 th)))>
#<alt (cos (+ ky (* -1 th)))>
#<alt (cos (+ ky (* -1 th)))>
#<alt (/ (* ky (sin th)) (sin kx))>
#<alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (sin th)>
#<alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))>
#<alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* 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)))))))>
#<alt (* 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))))))))))>
#<alt (* 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))))))))))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ ky (sin kx))>
#<alt (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))>
#<alt (* 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))))>
#<alt (* 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))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))>
#<alt (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (/ 1 ky)>
#<alt (/ (+ 1 (* 1/6 (pow ky 2))) ky)>
#<alt (/ (+ 1 (* (pow ky 2) (+ 1/6 (* 7/360 (pow ky 2))))) ky)>
#<alt (/ (+ 1 (* (pow ky 2) (+ 1/6 (* (pow ky 2) (+ 7/360 (* 31/15120 (pow ky 2))))))) ky)>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt (/ 1 (sin ky))>
#<alt ky>
#<alt (* ky (+ 1 (* -1/6 (pow ky 2))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))>
#<alt (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (sin ky)>
#<alt (cos th)>
#<alt (+ (cos th) (* -1 (* ky (sin th))))>
#<alt (+ (cos th) (* ky (- (* -1/2 (* ky (cos th))) (sin th))))>
#<alt (+ (cos th) (* ky (- (* ky (+ (* -1/2 (cos th)) (* 1/6 (* ky (sin th))))) (sin th))))>
#<alt (cos (+ ky th))>
#<alt (cos (+ ky th))>
#<alt (cos (+ ky th))>
#<alt (cos (+ ky th))>
#<alt (cos (- th (* -1 ky)))>
#<alt (cos (- th (* -1 ky)))>
#<alt (cos (- th (* -1 ky)))>
#<alt (cos (- th (* -1 ky)))>
#<alt (cos ky)>
#<alt (+ (cos ky) (* -1 (* th (sin ky))))>
#<alt (+ (cos ky) (* th (- (* -1/2 (* th (cos ky))) (sin ky))))>
#<alt (+ (cos ky) (* th (- (* th (+ (* -1/2 (cos ky)) (* 1/6 (* th (sin ky))))) (sin ky))))>
#<alt (cos (+ ky th))>
#<alt (cos (+ ky th))>
#<alt (cos (+ ky th))>
#<alt (cos (+ ky th))>
#<alt (cos (- ky (* -1 th)))>
#<alt (cos (- ky (* -1 th)))>
#<alt (cos (- ky (* -1 th)))>
#<alt (cos (- ky (* -1 th)))>

Calls

96 calls:

Time	Variable		Point	Expression
1.0ms	ky	@	0	(/ (* (- (cos (- ky th)) (cos (+ ky th))) 1) (* 2 (sin ky)))
1.0ms	ky	@	-inf	(/ (* (- (cos (- ky th)) (cos (+ ky th))) 1) (* 2 (sin ky)))
1.0ms	th	@	0	(/ (* (- (cos (- ky th)) (cos (+ ky th))) 1) (* 2 (sin ky)))
1.0ms	ky	@	inf	(/ (* (- (cos (- ky th)) (cos (+ ky th))) 1) (* 2 (sin ky)))
1.0ms	th	@	-inf	(/ (* (- (cos (- ky th)) (cos (+ ky th))) 1) (* 2 (sin ky)))

rewrite337.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4004×	`-lowering-.f32`
4004×	`-lowering-.f64`
3374×	`/-lowering-/.f32`
3374×	`/-lowering-/.f64`
1998×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	107
1	213	101
2	1558	101
0	8364	101

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 389

Calls

Call 1

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

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

simplify587.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

6716×	`-lowering-.f32`
6716×	`-lowering-.f64`
3328×	`+-lowering-+.f64`
3328×	`+-lowering-+.f32`
1542×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	632	5877
1	2186	5413
0	8133	5413

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

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

Outputs
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal 1/2 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))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (.f64 ky (.f64 ky (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 th) (sin.f64 kx))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))))) (+.f64 (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/5040 binary64)) (sin.f64 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 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)))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 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))))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(.f64 th (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (sin.f64 ky) (.f64 #s(literal -1/6 binary64) (.f64 th (*.f64 th (sin.f64 ky)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 th (+.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (.f64 (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 #s(literal 1/120 binary64) (.f64 th (*.f64 th (sin.f64 ky)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(.f64 th (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (sin.f64 ky) (.f64 #s(literal -1/6 binary64) (.f64 th (.f64 th (sin.f64 ky)))))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal -1/5040 binary64) (.f64 th (.f64 th (sin.f64 ky)))) (.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (.f64 (.f64 th th) (.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 ky (.f64 ky (+.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky (.f64 ky (+.f64 (.f64 (sin.f64 kx) (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))) #s(literal -1/2 binary64))) (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 (.f64 kx kx) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (.f64 kx kx)))) (.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+.f64 (sin.f64 ky) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (sin.f64 ky)))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+.f64 (sin.f64 ky) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(+.f64 (sin.f64 ky) (.f64 kx (.f64 kx (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (.f64 kx (.f64 kx (+.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (+.f64 #s(literal 2/45 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 ky)))))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+.f64 (sin.f64 kx) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (sin.f64 kx)))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+.f64 (sin.f64 kx) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (*.f64 ky ky) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(+.f64 (sin.f64 kx) (.f64 (.f64 ky ky) (+.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 kx)) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (+.f64 #s(literal 2/45 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 kx)))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal -1/6 binary64))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 ky ky) #s(literal 1/120 binary64))) ky) ky)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 ky ky) #s(literal -1/5040 binary64)))))))))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(/ (* kx (sin th)) (sin ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(* kx (+ (* -1/6 (/ (* (pow kx 2) (sin th)) (sin ky))) (/ (sin th) (sin ky))))
(.f64 kx (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal -1/6 binary64) (.f64 kx kx)) (sin.f64 th)) (sin.f64 ky))))
(* kx (+ (* (pow kx 2) (+ (* -1/6 (/ (sin th) (sin ky))) (* 1/120 (/ (* (pow kx 2) (sin th)) (sin ky))))) (/ (sin th) (sin ky))))
(.f64 kx (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal 1/120 binary64) (*.f64 kx kx)) (sin.f64 th)) (sin.f64 ky))))))
(* kx (+ (* (pow kx 2) (+ (* -1/6 (/ (sin th) (sin ky))) (* (pow kx 2) (+ (* -1/5040 (/ (* (pow kx 2) (sin th)) (sin ky))) (* 1/120 (/ (sin th) (sin ky))))))) (/ (sin th) (sin ky))))
(.f64 kx (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 kx (.f64 kx (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 ky)) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 #s(literal -1/5040 binary64) (.f64 kx kx)) (/.f64 (sin.f64 th) (sin.f64 ky))) (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 ky)))))))))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* th (sin kx)) (sin ky))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(* th (+ (* -1/6 (/ (* (pow th 2) (sin kx)) (sin ky))) (/ (sin kx) (sin ky))))
(.f64 th (+.f64 (/.f64 (sin.f64 kx) (sin.f64 ky)) (/.f64 (.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) (sin.f64 kx)) (sin.f64 ky))))
(* th (+ (* (pow th 2) (+ (* -1/6 (/ (sin kx) (sin ky))) (* 1/120 (/ (* (pow th 2) (sin kx)) (sin ky))))) (/ (sin kx) (sin ky))))
(.f64 th (+.f64 (/.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 (.f64 th th) (+.f64 (/.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (sin.f64 ky)) (.f64 (/.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 #s(literal 1/120 binary64) (*.f64 th th)))))))
(* th (+ (* (pow th 2) (+ (* -1/6 (/ (sin kx) (sin ky))) (* (pow th 2) (+ (* -1/5040 (/ (* (pow th 2) (sin kx)) (sin ky))) (* 1/120 (/ (sin kx) (sin ky))))))) (/ (sin kx) (sin ky))))
(.f64 th (+.f64 (/.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 (.f64 th th) (+.f64 (/.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (sin.f64 ky)) (.f64 (.f64 th th) (+.f64 (.f64 (.f64 #s(literal -1/5040 binary64) (.f64 th th)) (/.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (sin.f64 ky))))))))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/ (* (sin kx) (sin th)) (sin ky))
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(- (cos (neg (+ th (* -1 ky)))) (cos (- th (* -1 ky))))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(* th (- (sin ky) (* -1 (sin ky))))
(.f64 th (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(* th (- (+ (sin ky) (* (pow th 2) (- (* -1/6 (sin ky)) (* 1/6 (sin ky))))) (* -1 (sin ky))))
(.f64 th (+.f64 (.f64 (.f64 th (.f64 th (sin.f64 ky))) #s(literal -1/3 binary64)) (*.f64 #s(literal 2 binary64) (sin.f64 ky))))
(* th (- (+ (sin ky) (* (pow th 2) (- (+ (* -1/6 (sin ky)) (* (pow th 2) (- (* 1/120 (sin ky)) (* -1/120 (sin ky))))) (* 1/6 (sin ky))))) (* -1 (sin ky))))
(.f64 th (+.f64 (.f64 (.f64 th th) (+.f64 (.f64 th (.f64 th (.f64 (sin.f64 ky) #s(literal 1/60 binary64)))) (.f64 (sin.f64 ky) #s(literal -1/3 binary64)))) (.f64 #s(literal 2 binary64) (sin.f64 ky))))
(* th (- (+ (sin ky) (* (pow th 2) (- (+ (* -1/6 (sin ky)) (* (pow th 2) (- (+ (* 1/120 (sin ky)) (* (pow th 2) (- (* -1/5040 (sin ky)) (* 1/5040 (sin ky))))) (* -1/120 (sin ky))))) (* 1/6 (sin ky))))) (* -1 (sin ky))))
(.f64 th (+.f64 (.f64 (.f64 th th) (+.f64 (.f64 (.f64 th th) (+.f64 (.f64 (sin.f64 ky) (.f64 #s(literal -1/2520 binary64) (.f64 th th))) (.f64 (sin.f64 ky) #s(literal 1/60 binary64)))) (.f64 (sin.f64 ky) #s(literal -1/3 binary64)))) (*.f64 #s(literal 2 binary64) (sin.f64 ky))))
(- (cos (- ky th)) (cos (+ ky th)))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (- ky th)) (cos (+ ky th)))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (- ky th)) (cos (+ ky th)))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (- ky th)) (cos (+ ky th)))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(- (cos (+ ky (* -1 th))) (cos (- ky (* -1 th))))
(-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))
(cos (neg th))
(cos.f64 th)
(+ (cos (neg th)) (* -1 (* ky (sin (neg th)))))
(+.f64 (*.f64 ky (sin.f64 th)) (cos.f64 th))
(+ (cos (neg th)) (* ky (- (* -1/2 (* ky (cos (neg th)))) (sin (neg th)))))
(+.f64 (cos.f64 th) (.f64 ky (+.f64 (sin.f64 th) (.f64 ky (*.f64 #s(literal -1/2 binary64) (cos.f64 th))))))
(+ (cos (neg th)) (* ky (- (* ky (+ (* -1/2 (cos (neg th))) (* 1/6 (* ky (sin (neg th)))))) (sin (neg th)))))
(+.f64 (cos.f64 th) (.f64 ky (+.f64 (sin.f64 th) (.f64 ky (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 th)) (.f64 ky (*.f64 (sin.f64 th) #s(literal -1/6 binary64))))))))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (neg (+ th (* -1 ky))))
(cos.f64 (-.f64 th ky))
(cos (neg (+ th (* -1 ky))))
(cos.f64 (-.f64 th ky))
(cos (neg (+ th (* -1 ky))))
(cos.f64 (-.f64 th ky))
(cos (neg (+ th (* -1 ky))))
(cos.f64 (-.f64 th ky))
(cos ky)
(cos.f64 ky)
(+ (cos ky) (* th (sin ky)))
(+.f64 (*.f64 th (sin.f64 ky)) (cos.f64 ky))
(+ (cos ky) (* th (- (* -1/2 (* th (cos ky))) (* -1 (sin ky)))))
(+.f64 (cos.f64 ky) (.f64 th (+.f64 (sin.f64 ky) (.f64 th (*.f64 #s(literal -1/2 binary64) (cos.f64 ky))))))
(+ (cos ky) (* th (- (* th (+ (* -1/2 (cos ky)) (* -1/6 (* th (sin ky))))) (* -1 (sin ky)))))
(+.f64 (cos.f64 ky) (.f64 th (+.f64 (sin.f64 ky) (.f64 th (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 ky)) (.f64 th (*.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (- ky th))
(cos.f64 (-.f64 th ky))
(cos (+ ky (* -1 th)))
(cos.f64 (-.f64 th ky))
(cos (+ ky (* -1 th)))
(cos.f64 (-.f64 th ky))
(cos (+ ky (* -1 th)))
(cos.f64 (-.f64 th ky))
(cos (+ ky (* -1 th)))
(cos.f64 (-.f64 th ky))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal 1/2 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))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (.f64 ky (.f64 ky (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 th) (sin.f64 kx))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))))) (+.f64 (.f64 (.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/5040 binary64)) (sin.f64 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 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)))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 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))))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(.f64 th (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (sin.f64 ky) (.f64 #s(literal -1/6 binary64) (.f64 th (*.f64 th (sin.f64 ky)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 th (+.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (.f64 (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 #s(literal 1/120 binary64) (.f64 th (*.f64 th (sin.f64 ky)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(.f64 th (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (sin.f64 ky) (.f64 #s(literal -1/6 binary64) (.f64 th (.f64 th (sin.f64 ky)))))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal -1/5040 binary64) (.f64 th (.f64 th (sin.f64 ky)))) (.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (.f64 (.f64 th th) (.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 ky (.f64 ky (+.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky (.f64 ky (+.f64 (.f64 (sin.f64 kx) (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))) #s(literal -1/2 binary64))) (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 kx (.f64 kx (+.f64 (.f64 (.f64 kx kx) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (.f64 kx kx)))) (.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ 1 ky)
(/.f64 #s(literal 1 binary64) ky)
(/ (+ 1 (* 1/6 (pow ky 2))) ky)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* 7/360 (pow ky 2))))) ky)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 ky ky) #s(literal 7/360 binary64)))))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* (pow ky 2) (+ 7/360 (* 31/15120 (pow ky 2))))))) ky)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/6 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal 7/360 binary64) (.f64 (.f64 ky ky) #s(literal 31/15120 binary64)))))))) ky)
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal -1/6 binary64))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 ky ky) #s(literal 1/120 binary64))) ky) ky)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 ky ky) #s(literal -1/5040 binary64)))))))))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(cos th)
(cos.f64 th)
(+ (cos th) (* -1 (* ky (sin th))))
(-.f64 (cos.f64 th) (*.f64 ky (sin.f64 th)))
(+ (cos th) (* ky (- (* -1/2 (* ky (cos th))) (sin th))))
(+.f64 (cos.f64 th) (.f64 ky (-.f64 (.f64 ky (*.f64 #s(literal -1/2 binary64) (cos.f64 th))) (sin.f64 th))))
(+ (cos th) (* ky (- (* ky (+ (* -1/2 (cos th)) (* 1/6 (* ky (sin th))))) (sin th))))
(+.f64 (cos.f64 th) (.f64 ky (-.f64 (.f64 ky (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 th)) (.f64 ky (*.f64 (sin.f64 th) #s(literal 1/6 binary64))))) (sin.f64 th))))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (- th (* -1 ky)))
(cos.f64 (+.f64 ky th))
(cos (- th (* -1 ky)))
(cos.f64 (+.f64 ky th))
(cos (- th (* -1 ky)))
(cos.f64 (+.f64 ky th))
(cos (- th (* -1 ky)))
(cos.f64 (+.f64 ky th))
(cos ky)
(cos.f64 ky)
(+ (cos ky) (* -1 (* th (sin ky))))
(-.f64 (cos.f64 ky) (*.f64 th (sin.f64 ky)))
(+ (cos ky) (* th (- (* -1/2 (* th (cos ky))) (sin ky))))
(+.f64 (cos.f64 ky) (.f64 th (-.f64 (.f64 th (*.f64 #s(literal -1/2 binary64) (cos.f64 ky))) (sin.f64 ky))))
(+ (cos ky) (* th (- (* th (+ (* -1/2 (cos ky)) (* 1/6 (* th (sin ky))))) (sin ky))))
(+.f64 (cos.f64 ky) (.f64 th (-.f64 (.f64 th (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 ky)) (.f64 th (*.f64 (sin.f64 ky) #s(literal 1/6 binary64))))) (sin.f64 ky))))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (+ ky th))
(cos.f64 (+.f64 ky th))
(cos (- ky (* -1 th)))
(cos.f64 (+.f64 ky th))
(cos (- ky (* -1 th)))
(cos.f64 (+.f64 ky th))
(cos (- ky (* -1 th)))
(cos.f64 (+.f64 ky th))
(cos (- ky (* -1 th)))
(cos.f64 (+.f64 ky th))

eval127.0ms (1%)

Compiler: Compiled 22692 to 2357 computations (89.6% saved)

prune154.0ms (1.2%)

Pruning

69 alts after pruning (62 fresh and 7 done)

	Pruned	Kept	Total
New	1016	29	1045
Fresh	10	33	43
Picked	2	3	5
Done	0	4	4
Total	1028	69	1097

Accuracy

100.0%

Counts

1097 → 69

Alt Table

Click to see full alt table

Status	Accuracy	Program
	12.8%	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 th)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	12.7%	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 ky)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	13.5%	(/.f64 (.f64 (-.f64 (cos.f64 th) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	12.8%	(/.f64 (.f64 (-.f64 (cos.f64 ky) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	4.3%	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
▶	5.1%	(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
	96.6%	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	36.0%	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
	4.9%	(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
	33.9%	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
▶	99.6%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	30.2%	(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
	96.1%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
	35.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
	11.9%	(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
▶	46.6%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
	62.0%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
	69.2%	(.f64 (/.f64 (sin.f64 ky) (pow.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sin.f64 th))
	65.7%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky)))) (sin.f64 th))
✓	99.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))) (sin.f64 th))
	99.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th))))
	99.4%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
	79.4%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))))
	45.9%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))))
✓	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
	46.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
	62.1%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
	60.0%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 kx (sin.f64 ky))) (sin.f64 th))
✓	44.3%	(*.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))))) th)
	69.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	38.1%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
	18.9%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
	35.5%	(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
	17.6%	(*.f64 (/.f64 ky (sin.f64 kx)) th)
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	35.9%	(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
	99.4%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) (sin.f64 th))
	23.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
	99.6%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
	6.5%	(.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
	60.7%	(.f64 (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	4.3%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
	60.1%	(.f64 (sin.f64 ky) (/.f64 (.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (sin.f64 ky)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 th)))) (hypot.f64 ky (sin.f64 kx))))
	60.6%	(.f64 (sin.f64 ky) (/.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))) (hypot.f64 ky (sin.f64 kx))))
	20.8%	(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
✓	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
▶	30.2%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	38.1%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
	20.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
	46.6%	(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	29.7%	(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
	30.1%	(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
	4.2%	(.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal -1/2 binary64))))
✓	6.1%	(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
	4.4%	(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
	6.1%	(*.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sin.f64 th))))
	14.6%	(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
	14.6%	(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
	70.3%	(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	20.7%	(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
	17.5%	(*.f64 ky (/.f64 th (sin.f64 kx)))
	4.7%	(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
	36.0%	(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
	14.6%	(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64)))) (sin.f64 ky)))
✓	30.3%	(sin.f64 th)
✓	15.0%	th
▶	12.5%	#s(literal 0 binary64)

Compiler

Compiled 1974 to 1351 computations (31.6% saved)

simplify347.0ms (2.8%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	cost-diff	256	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	cost-diff	256	(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
✓	cost-diff	13312	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(*.f64 (sin.f64 th) kx)
✓	cost-diff	0	(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
✓	cost-diff	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	cost-diff	0	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Rules

8034×	`-lowering-.f32`
8034×	`-lowering-.f64`
3918×	`associate-/r/`
3778×	`/-lowering-/.f32`
3778×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	107
1	54	107
2	124	107
3	219	107
4	377	107
5	999	107
6	1635	107
7	2003	107
8	2154	107
9	2259	107
10	2425	107
11	2667	107
12	2986	107
13	3379	107
14	3875	107
15	4446	107
16	4662	107
17	4766	107
18	4852	107
19	4918	107
20	4984	107
21	5504	107
22	6369	107
0	10305	107

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)))
(sin th)
th
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
(sin ky)
ky
(sin kx)
kx
0
(/ (* (sin th) kx) (sin ky))
(* (sin th) kx)
(sin th)
th
kx
(sin ky)
ky
(* (sin ky) (/ (sin th) (/ 1 (/ 1 (sin ky)))))
(sin ky)
ky
(/ (sin th) (/ 1 (/ 1 (sin ky))))
(sin th)
th
(/ 1 (/ 1 (sin ky)))
1
(/ 1 (sin ky))
(* (/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) th)
(/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
(/ 1 (/ 1 (sin ky)))
1
(/ 1 (sin ky))
(sin ky)
ky
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
(sin kx)
kx
th

Outputs
(/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(sin th)
(sin.f64 th)
th
(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin ky)
(sin.f64 ky)
ky
(sin kx)
(sin.f64 kx)
kx
0
#s(literal 0 binary64)
(/ (* (sin th) kx) (sin ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(* (sin th) kx)
(*.f64 (sin.f64 th) kx)
(sin th)
(sin.f64 th)
th
kx
(sin ky)
(sin.f64 ky)
ky
(* (sin ky) (/ (sin th) (/ 1 (/ 1 (sin ky)))))
(sin.f64 th)
(sin ky)
(sin.f64 ky)
ky
(/ (sin th) (/ 1 (/ 1 (sin ky))))
(/.f64 (sin.f64 th) (sin.f64 ky))
(sin th)
(sin.f64 th)
th
(/ 1 (/ 1 (sin ky)))
(sin.f64 ky)
1
#s(literal 1 binary64)
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(* (/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) th)
(/.f64 th (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/ 1 (/ 1 (sin ky)))
(sin.f64 ky)
1
#s(literal 1 binary64)
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(sin ky)
(sin.f64 ky)
ky
(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin kx)
(sin.f64 kx)
kx
th

localize145.0ms (1.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
✓	accuracy	99.8%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
✓	accuracy	99.8%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
✓	accuracy	99.7%	(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓	accuracy	99.7%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
✓	accuracy	100.0%	(sin.f64 th)
✓	accuracy	100.0%	(sin.f64 ky)
✓	accuracy	99.8%	(*.f64 (sin.f64 th) kx)
✓	accuracy	95.7%	(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
✓	accuracy	100.0%	(sin.f64 kx)
✓	accuracy	99.9%	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	accuracy	99.8%	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	accuracy	99.7%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Results

91.0ms

256×

valid

Compiler

Compiled 143 to 21 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-sin: 27.0ms (37.2% of total)

ival-mult: 14.0ms (19.3% of total)

compiled-spec: 14.0ms (19.3% of total)

ival-div: 11.0ms (15.2% of total)

ival-sqrt: 4.0ms (5.5% of total)

ival-add: 2.0ms (2.8% of total)

const: 1.0ms (1.4% of total)

backward-pass: 0.0ms (0% of total)

series31.0ms (0.2%)

Counts

14 → 312

Calls

Call 1

Inputs
#<alt (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)))>
#<alt (sin th)>
#<alt (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))>
#<alt (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))>
#<alt (/ (* (sin th) kx) (sin ky))>
#<alt (* (sin th) kx)>
#<alt (sin ky)>
#<alt (* (sin ky) (/ (sin th) (/ 1 (/ 1 (sin ky)))))>
#<alt (/ (sin th) (/ 1 (/ 1 (sin ky))))>
#<alt (/ 1 (/ 1 (sin ky)))>
#<alt (* (/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) th)>
#<alt (/ (/ 1 (/ 1 (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))>
#<alt (/ 1 (sin ky))>
#<alt (sin kx)>

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

Calls

78 calls:

Time	Variable		Point	Expression
2.0ms	th	@	0	(/ (* (sin th) kx) (sin ky))
1.0ms	ky	@	0	(/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))
1.0ms	kx	@	0	(/ (* (sin th) kx) (sin ky))
1.0ms	th	@	-inf	(/ (* (sin th) kx) (sin ky))
1.0ms	th	@	inf	(/ (* (sin th) kx) (sin ky))

rewrite310.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2326×	`-lowering-.f32`
2326×	`-lowering-.f64`
2094×	`/-lowering-/.f32`
2094×	`/-lowering-/.f64`
910×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	153	71
2	1064	71
0	9506	71

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 455

Calls

Call 1

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

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

simplify379.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

7054×	`-lowering-.f32`
7054×	`-lowering-.f64`
3032×	`+-lowering-+.f64`
3032×	`+-lowering-+.f32`
1550×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	563	4385
1	1991	4081
0	8395	4081

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

Outputs
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(.f64 th (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) (sin.f64 ky)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 th (+.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (.f64 (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) (sin.f64 ky)) (*.f64 (sin.f64 ky) #s(literal -1/6 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))))))))))))
(.f64 th (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) (sin.f64 ky)) (sin.f64 ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 (.f64 th th) #s(literal -1/5040 binary64)) (sin.f64 ky)) (.f64 (sin.f64 ky) #s(literal 1/120 binary64)))) (.f64 (.f64 th th) (.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (/.f64 (.f64 #s(literal 1/120 binary64) (sin.f64 th)) (sin.f64 kx))))))))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(.f64 ky (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx)) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 ky (.f64 ky (+.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))))) (+.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 kx) (sin.f64 th))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))))) (+.f64 (.f64 (.f64 (.f64 (sin.f64 kx) #s(literal -1/12 binary64)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/240 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx)))))) (/.f64 (*.f64 #s(literal 1/120 binary64) (sin.f64 th)) (sin.f64 kx)))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+.f64 (sin.f64 th) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 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)))))))))))
(+.f64 (sin.f64 th) (.f64 kx (.f64 kx (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 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))))))))))))
(+.f64 (sin.f64 th) (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
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(* th (+ kx (* (pow th 2) (+ (* -1/6 kx) (* (pow th 2) (+ (* -1/5040 (* kx (pow th 2))) (* 1/120 kx)))))))
(.f64 th (+.f64 kx (.f64 (.f64 th th) (+.f64 (.f64 kx #s(literal -1/6 binary64)) (.f64 (.f64 th th) (+.f64 (.f64 kx (.f64 (.f64 th th) #s(literal -1/5040 binary64))) (.f64 kx #s(literal 1/120 binary64))))))))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
(* kx (sin th))
(*.f64 kx (sin.f64 th))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (*.f64 ky #s(literal -1/6 binary64)))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 ky ky))) ky) ky)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (*.f64 ky #s(literal -1/5040 binary64))))))))))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 th th) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 th th) #s(literal 1/120 binary64))))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 th th) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 th th) #s(literal -1/5040 binary64))))))))
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(/ th (sin ky))
(/.f64 th (sin.f64 ky))
(* th (+ (* -1/6 (/ (pow th 2) (sin ky))) (/ 1 (sin ky))))
(.f64 th (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) (sin.f64 ky))))
(* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin ky))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))
(.f64 th (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (.f64 th th) (+.f64 (/.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (/.f64 (.f64 (*.f64 th th) #s(literal 1/120 binary64)) (sin.f64 ky))))))
(* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin ky))) (* 1/120 (/ 1 (sin ky))))) (* 1/6 (/ 1 (sin ky))))) (/ 1 (sin ky))))
(.f64 th (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (.f64 th th) (+.f64 (.f64 (.f64 th th) (+.f64 (/.f64 (.f64 (*.f64 th th) #s(literal -1/5040 binary64)) (sin.f64 ky)) (/.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (/.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) ky)
(/.f64 (sin.f64 th) ky)
(/ (+ (sin th) (* 1/6 (* (pow ky 2) (sin th)))) ky)
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) (sin.f64 th)) ky)
(/ (+ (sin th) (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) ky)
(/.f64 (+.f64 (sin.f64 th) (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 ky ky) (.f64 (sin.f64 th) #s(literal 7/360 binary64))) (.f64 (sin.f64 th) #s(literal 1/6 binary64))))) ky)
(/ (+ (sin th) (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 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))))) ky)
(/.f64 (+.f64 (sin.f64 th) (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (.f64 (sin.f64 th) #s(literal -7/2160 binary64)) (.f64 (sin.f64 th) #s(literal 1/840 binary64))) (.f64 (.f64 ky ky) #s(literal -1 binary64))) (.f64 (sin.f64 th) #s(literal 7/360 binary64)))) (*.f64 (sin.f64 th) #s(literal 1/6 binary64))))) ky)
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (*.f64 ky #s(literal -1/6 binary64)))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 ky ky))) ky) ky)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (*.f64 ky #s(literal -1/5040 binary64))))))))))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(/ (* ky th) (sin kx))
(*.f64 th (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))
(.f64 ky (+.f64 (/.f64 th (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (/.f64 (.f64 th #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 th #s(literal -1/6 binary64)) (sin.f64 kx)))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
(.f64 ky (+.f64 (/.f64 th (sin.f64 kx)) (.f64 ky (.f64 ky (+.f64 (+.f64 (/.f64 (.f64 th #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 th #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky (.f64 ky (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 th (sin.f64 kx))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (+.f64 (/.f64 (.f64 th #s(literal 1/120 binary64)) (sin.f64 kx)) (/.f64 (.f64 th #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
(.f64 ky (+.f64 (/.f64 th (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 (.f64 th #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 th #s(literal -1/6 binary64)) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 th (sin.f64 kx))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (+.f64 (/.f64 (.f64 th #s(literal 1/120 binary64)) (sin.f64 kx)) (/.f64 (.f64 th #s(literal 1/12 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 (.f64 ky ky) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (sin.f64 kx))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))))) (+.f64 (.f64 (.f64 (.f64 th #s(literal -1/12 binary64)) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (+.f64 (.f64 #s(literal -1/240 binary64) (/.f64 th (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 #s(literal -1/5040 binary64) (/.f64 th (sin.f64 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+.f64 th (.f64 kx (.f64 kx (+.f64 (/.f64 (.f64 th #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx (.f64 kx (.f64 (.f64 #s(literal 1/2 binary64) (.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(+.f64 th (.f64 (.f64 kx kx) (+.f64 (/.f64 (.f64 th #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 (.f64 ky ky) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 ky (+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (-.f64 (.f64 ky (.f64 ky (+.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky (.f64 ky (+.f64 (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))))) (.f64 (sin.f64 kx) #s(literal -1/2 binary64))) (-.f64 (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 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))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx (.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 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))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 kx kx) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx (.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))) (.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ 1 ky)
(/.f64 #s(literal 1 binary64) ky)
(/ (+ 1 (* 1/6 (pow ky 2))) ky)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* 7/360 (pow ky 2))))) ky)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 ky ky) #s(literal 7/360 binary64)))))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* (pow ky 2) (+ 7/360 (* 31/15120 (pow ky 2))))))) ky)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 7/360 binary64) (.f64 (.f64 ky ky) #s(literal 31/15120 binary64))))))) ky)
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(.f64 kx (+.f64 #s(literal 1 binary64) (.f64 kx (*.f64 kx #s(literal -1/6 binary64)))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(.f64 kx (+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (+.f64 #s(literal -1/6 binary64) (.f64 kx (*.f64 kx #s(literal 1/120 binary64)))))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(.f64 kx (+.f64 #s(literal 1 binary64) (.f64 (.f64 kx kx) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 kx kx) (+.f64 #s(literal 1/120 binary64) (.f64 kx (*.f64 kx #s(literal -1/5040 binary64)))))))))
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)

eval201.0ms (1.6%)

Compiler: Compiled 19695 to 2326 computations (88.2% saved)

prune242.0ms (2%)

Pruning

81 alts after pruning (70 fresh and 11 done)

	Pruned	Kept	Total
New	1163	31	1194
Fresh	18	39	57
Picked	0	5	5
Done	1	6	7
Total	1182	81	1263

Accuracy

100.0%

Counts

1263 → 81

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	5.1%	(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
	99.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	12.8%	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 th)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	12.7%	(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 ky)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	13.5%	(/.f64 (.f64 (-.f64 (cos.f64 th) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	12.8%	(/.f64 (.f64 (-.f64 (cos.f64 ky) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
	3.6%	(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
	36.0%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sin.f64 ky))
	4.6%	(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
	4.6%	(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
✓	5.1%	(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
	45.9%	(/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	43.6%	(/.f64 (*.f64 th (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	4.1%	(/.f64 (*.f64 th kx) (sin.f64 ky))
	33.9%	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
✓	99.6%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	61.1%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) ky))
	4.7%	(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
	38.1%	(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
	35.5%	(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
	99.5%	(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	33.1%	(/.f64 (sin.f64 th) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
	99.5%	(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
	79.4%	(/.f64 (sin.f64 th) (*.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
	99.6%	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	30.2%	(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
	46.7%	(/.f64 th (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	4.7%	(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
	96.1%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	46.0%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) th))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
	35.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
	11.9%	(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	46.6%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
	62.0%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
	32.3%	(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th)
	65.7%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky)))) (sin.f64 th))
✓	99.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))) (sin.f64 th))
✓	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
	62.1%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
	60.0%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 kx (sin.f64 ky))) (sin.f64 th))
✓	44.3%	(*.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))))) th)
	38.1%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
	18.9%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
	46.6%	(*.f64 (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
	28.7%	(*.f64 (/.f64 ky (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
	35.5%	(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
	17.6%	(*.f64 (/.f64 ky (sin.f64 kx)) th)
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	35.9%	(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
	5.1%	(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
	99.6%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
	6.5%	(.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
	60.7%	(.f64 (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	4.3%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
	20.8%	(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
	20.8%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
✓	30.2%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	38.1%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
	20.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
	29.7%	(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
	14.9%	(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	30.1%	(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
	4.2%	(.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal -1/2 binary64))))
✓	6.1%	(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
	4.4%	(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
	6.1%	(*.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sin.f64 th))))
	3.7%	(*.f64 th (/.f64 kx (sin.f64 ky)))
	14.6%	(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
	14.6%	(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
	70.3%	(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
	20.7%	(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	20.7%	(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
	17.5%	(*.f64 ky (/.f64 th (sin.f64 kx)))
	36.0%	(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
	14.6%	(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64)))) (sin.f64 ky)))
✓	30.3%	(sin.f64 th)
✓	15.0%	th
✓	12.5%	#s(literal 0 binary64)

Compiler

Compiled 2612 to 1132 computations (56.7% saved)

regimes371.0ms (3%)

Counts

117 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 ky (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(*.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
(.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th)
(/.f64 (.f64 (-.f64 (cos.f64 ky) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 th) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 ky)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 th)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(/.f64 (sin.f64 th) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))) (hypot.f64 ky (sin.f64 kx))))
(.f64 (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64)))) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) kx)))
(*.f64 (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 kx (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(/.f64 th (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) ky))
(/.f64 (*.f64 th (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal -1/2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) th) th))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))))
(/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 ky (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64))))))))) th)
(*.f64 (exp.f64 (log.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))) (sin.f64 th))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (.f64 ky (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (pow.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 (/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th)))))
(/.f64 (sin.f64 th) (*.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))) (hypot.f64 ky (sin.f64 kx))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (sin.f64 ky)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 th)))) (hypot.f64 ky (sin.f64 kx))))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))))

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

Calls

9 calls:

55.0ms	kx
49.0ms	(sin.f64 th)
48.0ms	ky
37.0ms	(sin.f64 kx)
36.0ms	(sin.f64 ky)

Results

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

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes208.0ms (1.7%)

Counts

86 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 ky (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(*.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
(.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th)
(/.f64 (.f64 (-.f64 (cos.f64 ky) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 th) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 ky)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 th)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(/.f64 (sin.f64 th) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))) (hypot.f64 ky (sin.f64 kx))))
(.f64 (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64)))) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) kx)))
(*.f64 (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 kx (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(/.f64 th (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) ky))
(/.f64 (*.f64 th (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal -1/2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) th) th))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))))
(/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 ky (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64))))))))) th)
(*.f64 (exp.f64 (log.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

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

Calls

7 calls:

36.0ms	(sin.f64 th)
32.0ms	kx
32.0ms	(sin.f64 kx)
27.0ms	th
24.0ms	(sin.f64 ky)

Results

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

Compiler

Compiled 34 to 27 computations (20.6% saved)

regimes239.0ms (1.9%)

Counts

85 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 ky (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(*.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
(.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th)
(/.f64 (.f64 (-.f64 (cos.f64 ky) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 th) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 ky)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 th)) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(/.f64 (sin.f64 th) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (.f64 #s(literal 2 binary64) (sin.f64 ky)))
(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))) (hypot.f64 ky (sin.f64 kx))))
(.f64 (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 (-.f64 ky th) ky) th) #s(literal 2 binary64)))) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) kx)))
(*.f64 (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 kx (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(/.f64 th (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) ky))
(/.f64 (*.f64 th (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) ky)) (sin.f64 th))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))) #s(literal -1/2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) th) th))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))))
(/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 ky (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) (+.f64 (.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64))))))))) th)
(*.f64 (exp.f64 (log.f64 (sin.f64 ky))) (/.f64 (sin.f64 th) (sin.f64 ky)))

Outputs

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

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

Calls

7 calls:

43.0ms	(sin.f64 ky)
41.0ms	(sin.f64 th)
34.0ms	(sin.f64 kx)
30.0ms	th
25.0ms	ky

Results

Accuracy	Segments	Branch
83.5%	2	`kx`
82.1%	3	`ky`
84.6%	2	`th`
80.4%	2	`(sin.f64 ky)`
83.5%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
83.5%	3	`(sin.f64 kx)`
84.6%	3	`(sin.f64 th)`

Compiler

Compiled 34 to 27 computations (20.6% saved)

regimes32.0ms (0.3%)

Counts

80 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

24.0ms

th

Results

Accuracy	Segments	Branch
84.6%	2	`th`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes30.0ms (0.2%)

Counts

79 → 2

Calls

Call 1

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

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

Calls

1 calls:

23.0ms

th

Results

Accuracy	Segments	Branch
84.4%	2	`th`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes29.0ms (0.2%)

Counts

70 → 2

Calls

Call 1

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

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

Calls

1 calls:

23.0ms

th

Results

Accuracy	Segments	Branch
84.4%	2	`th`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes119.0ms (1%)

Counts

64 → 2

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th)
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))

Calls

6 calls:

19.0ms	(sin.f64 th)
19.0ms	(sin.f64 ky)
19.0ms	(sin.f64 kx)
19.0ms	th
18.0ms	kx

Results

Accuracy	Segments	Branch
75.9%	2	`(sin.f64 ky)`
72.6%	2	`ky`
70.3%	1	`(sin.f64 kx)`
73.7%	3	`(sin.f64 th)`
70.3%	1	`kx`
73.4%	2	`th`

Compiler

Compiled 27 to 21 computations (22.2% saved)

regimes75.0ms (0.6%)

Counts

53 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(*.f64 (sin.f64 ky) (/.f64 th (hypot.f64 ky (sin.f64 kx))))
(*.f64 (/.f64 ky (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th)
(*.f64 (sin.f64 kx) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sin.f64 th)))
(.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))))

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

Calls

4 calls:

17.0ms	(sin.f64 th)
16.0ms	(sin.f64 ky)
16.0ms	ky
15.0ms	th

Results

Accuracy	Segments	Branch
70.3%	1	`(sin.f64 th)`
70.3%	1	`ky`
70.3%	1	`th`
70.3%	1	`(sin.f64 ky)`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes87.0ms (0.7%)

Counts

43 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sin.f64 ky))

Outputs
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

Calls

6 calls:

16.0ms	th
16.0ms	(sin.f64 ky)
13.0ms	(sin.f64 kx)
13.0ms	kx
13.0ms	ky

Results

Accuracy	Segments	Branch
51.4%	2	`ky`
52.7%	2	`(sin.f64 ky)`
53.1%	2	`kx`
53.4%	2	`(sin.f64 kx)`
42.3%	2	`th`
45.1%	4	`(sin.f64 th)`

Compiler

Compiled 27 to 21 computations (22.2% saved)

regimes15.0ms (0.1%)

Counts

38 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 ky)))

Outputs
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))

Calls

1 calls:

12.0ms

(sin.f64 kx)

Results

Accuracy	Segments	Branch
53.4%	2	`(sin.f64 kx)`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes65.0ms (0.5%)

Counts

36 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))
(+.f64 th (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 th (*.f64 kx kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(.f64 (sin.f64 ky) (/.f64 (.f64 (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) ky))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal 1/6 binary64))) (.f64 (sin.f64 th) (sin.f64 kx))) ky)
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal 1/6 binary64))) ky))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (sin.f64 ky)))

Outputs
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky))

Calls

4 calls:

29.0ms	ky
12.0ms	kx
11.0ms	(sin.f64 kx)
10.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
51.4%	2	`ky`
51.3%	2	`(sin.f64 ky)`
50.8%	2	`kx`
51.1%	2	`(sin.f64 kx)`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes42.0ms (0.3%)

Counts

30 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) th)
(/.f64 kx (/.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 ky) kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(/.f64 (*.f64 th (sin.f64 kx)) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) kx) (sin.f64 ky))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (sin.f64 th) kx))
(/.f64 (/.f64 kx (/.f64 #s(literal 1 binary64) (sin.f64 th))) (sin.f64 ky))
(*.f64 ky (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 th (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))

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

Calls

4 calls:

11.0ms	(sin.f64 ky)
11.0ms	kx
9.0ms	ky
9.0ms	(sin.f64 kx)

Results

Accuracy	Segments	Branch
50.8%	2	`kx`
51.2%	3	`(sin.f64 kx)`
49.9%	2	`(sin.f64 ky)`
50.0%	2	`ky`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes39.0ms (0.3%)

Counts

18 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(/.f64 (*.f64 th kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky #s(literal -1/6 binary64))))))
(/.f64 (.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) kx) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) kx) (.f64 ky (+.f64 #s(literal 1 binary64) (.f64 ky (.f64 ky (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) (+.f64 #s(literal 1/120 binary64) (.f64 ky (.f64 ky #s(literal -1/5040 binary64)))))))))))
(*.f64 kx (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 ky (/.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 kx) (/.f64 th (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) ky))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))

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

Calls

6 calls:

8.0ms	kx
6.0ms	(sin.f64 kx)
6.0ms	th
6.0ms	(sin.f64 ky)
6.0ms	ky

Results

Accuracy	Segments	Branch
36.4%	3	`(sin.f64 th)`
36.4%	2	`th`
37.7%	3	`(sin.f64 kx)`
36.5%	2	`(sin.f64 ky)`
36.6%	2	`ky`
37.2%	2	`kx`

Compiler

Compiled 27 to 21 computations (22.2% saved)

regimes4.0ms (0%)

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)
(*.f64 ky (/.f64 th (sin.f64 kx)))
(*.f64 th (/.f64 kx (sin.f64 ky)))

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

Calls

1 calls:

3.0ms

kx

Results

Accuracy	Segments	Branch
37.2%	2	`kx`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes9.0ms (0.1%)

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(sin.f64 th)

Outputs
(sin.f64 th)
#s(literal 0 binary64)

Calls

3 calls:

3.0ms	kx
2.0ms	ky
2.0ms	th

Results

Accuracy	Segments	Branch
33.6%	2	`th`
33.3%	2	`ky`
35.4%	2	`kx`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.1%)

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
th
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))
(.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (*.f64 th #s(literal -1/6 binary64)))))

Outputs
th
#s(literal 0 binary64)

Calls

3 calls:

2.0ms	kx
2.0ms	ky
2.0ms	th

Results

Accuracy	Segments	Branch
19.8%	2	`ky`
18.4%	2	`th`
21.8%	2	`kx`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

3 calls:

2.0ms	th
1.0ms	kx
1.0ms	ky

Results

Accuracy	Segments	Branch
12.5%	1	`th`
12.5%	1	`ky`
12.5%	1	`kx`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch35.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
32.0ms	0.00011848184033961039	1972487.6144006983

Results

22.0ms

160×

valid

Compiler

Compiled 375 to 258 computations (31.2% saved)

Precisions

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

ival-sin: 8.0ms (49.9% of total)

ival-pow: 3.0ms (18.7% of total)

ival-div: 1.0ms (6.2% of total)

ival-add: 1.0ms (6.2% of total)

ival-mult: 1.0ms (6.2% of total)

ival-sqrt: 1.0ms (6.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch33.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
30.0ms	0.00011848184033961039	1972487.6144006983

Results

25.0ms

160×

valid

Compiler

Compiled 375 to 258 computations (31.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sin: 12.0ms (62.6% of total)

ival-pow: 3.0ms (15.6% of total)

ival-div: 1.0ms (5.2% of total)

ival-add: 1.0ms (5.2% of total)

ival-mult: 1.0ms (5.2% of total)

ival-sqrt: 1.0ms (5.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch32.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	0.00011848184033961039	1972487.6144006983

Results

24.0ms

160×

valid

Compiler

Compiled 295 to 198 computations (32.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sin: 8.0ms (44.1% of total)

ival-mult: 3.0ms (16.5% of total)

ival-pow: 3.0ms (16.5% of total)

ival-div: 1.0ms (5.5% of total)

ival-add: 1.0ms (5.5% of total)

ival-sqrt: 1.0ms (5.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch36.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
34.0ms	0.00011848184033961039	1972487.6144006983

Results

28.0ms

160×

valid

Compiler

Compiled 295 to 198 computations (32.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sin: 8.0ms (45.5% of total)

ival-sqrt: 3.0ms (17.1% of total)

ival-pow: 3.0ms (17.1% of total)

ival-div: 1.0ms (5.7% of total)

ival-add: 1.0ms (5.7% of total)

ival-mult: 1.0ms (5.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.07418747289317305	-0.024348770471462704

Compiler

Compiled 24 to 18 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.228886037019633e-105	2.2094033658493293e-104

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.228886037019633e-105	2.2094033658493293e-104

Compiler

Compiled 25 to 18 computations (28% saved)

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	5.029535988246529e-99	9.358301033996719e-97

Results

17.0ms

112×

valid

Compiler

Compiled 221 to 158 computations (28.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 6.0ms (54% of total)

ival-pow: 2.0ms (18% of total)

ival-div: 1.0ms (9% of total)

ival-add: 1.0ms (9% of total)

ival-mult: 1.0ms (9% of total)

ival-sqrt: 1.0ms (9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch16.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	9.228886037019633e-105	2.2094033658493293e-104

Results

12.0ms

80×

valid

Compiler

Compiled 110 to 83 computations (24.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sin: 5.0ms (53.9% of total)

ival-pow: 2.0ms (21.6% of total)

ival-div: 1.0ms (10.8% of total)

ival-mult: 1.0ms (10.8% of total)

ival-sqrt: 1.0ms (10.8% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch31.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	179316.6483050387	1825222946.4580195

Results

25.0ms

128×

valid

Compiler

Compiled 153 to 114 computations (25.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sin: 14.0ms (69.5% of total)

ival-pow: 3.0ms (14.9% of total)

ival-div: 1.0ms (5% of total)

ival-add: 1.0ms (5% of total)

ival-mult: 1.0ms (5% of total)

ival-sqrt: 1.0ms (5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch29.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	179316.6483050387	1825222946.4580195

Results

23.0ms

128×

valid

Compiler

Compiled 153 to 114 computations (25.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-sin: 11.0ms (63.7% of total)

ival-pow: 3.0ms (17.4% of total)

ival-div: 1.0ms (5.8% of total)

ival-add: 1.0ms (5.8% of total)

ival-mult: 1.0ms (5.8% of total)

ival-sqrt: 1.0ms (5.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch33.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	3.1046658150242965e+25	1.0993384032459305e+32

Results

24.0ms

144×

valid

Compiler

Compiled 124 to 108 computations (12.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sin: 12.0ms (64.2% of total)

ival-pow: 3.0ms (16% of total)

ival-div: 1.0ms (5.3% of total)

ival-add: 1.0ms (5.3% of total)

ival-mult: 1.0ms (5.3% of total)

ival-sqrt: 1.0ms (5.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	7.380206857091753e-39	2.8351632142690118e-37

Results

15.0ms

112×

valid

Compiler

Compiled 95 to 81 computations (14.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 6.0ms (54.8% of total)

ival-pow: 2.0ms (18.3% of total)

ival-div: 1.0ms (9.1% of total)

ival-add: 1.0ms (9.1% of total)

ival-mult: 1.0ms (9.1% of total)

ival-sqrt: 1.0ms (9.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`+-rgt-identity_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	287
1	116	287

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.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 ky) (sin.f64 kx))))
(if (<=.f64 th #s(literal 1988789595446811/288230376151711744 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64)))))) (*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 1642913144064757/288230376151711744 binary64)) (.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) th) th))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 5418731071652181/2305843009213693952 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 9002011107970261/73786976294838206464 binary64)) (.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 (sin.f64 ky) #s(literal -3602879701896397/72057594037927936 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(if (<=.f64 (sin.f64 kx) #s(literal 6455624695217271/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky)) (*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
(if (<=.f64 (sin.f64 kx) #s(literal 6455624695217271/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(if (<=.f64 ky #s(literal 4040244775997481/9619630419041620901435312524449124464130795720328478190417063819395928166869436184427311097384012607618805661696 binary64)) (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky)))
(if (<=.f64 kx #s(literal 5325890373554249/322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672 binary64)) (sin.f64 th) (*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th)))
(if (<=.f64 kx #s(literal 380000 binary64)) (sin.f64 th) (*.f64 (/.f64 ky (sin.f64 kx)) th))
(if (<=.f64 kx #s(literal 180000 binary64)) (sin.f64 th) (*.f64 ky (/.f64 th (sin.f64 kx))))
(if (<=.f64 kx #s(literal 31499999999999998666211328 binary64)) (sin.f64 th) #s(literal 0 binary64))
(if (<=.f64 kx #s(literal 838083498911033/11972621413014756705924586149611790497021399392059392 binary64)) th #s(literal 0 binary64))
#s(literal 0 binary64)

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 ky) (sin.f64 kx))))
(if (<=.f64 th #s(literal 1988789595446811/288230376151711744 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64)))))) (*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 1642913144064757/288230376151711744 binary64)) (.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/6 binary64) th) th))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 1642913144064757/288230376151711744 binary64)) (.f64 (sin.f64 ky) (/.f64 (.f64 th (+.f64 #s(literal 1 binary64) (.f64 th (.f64 th #s(literal -1/6 binary64))))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 5418731071652181/2305843009213693952 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) th) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 th #s(literal 9002011107970261/73786976294838206464 binary64)) (.f64 (sin.f64 ky) (/.f64 th (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 (sin.f64 ky) #s(literal -3602879701896397/72057594037927936 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky))) th) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(if (<=.f64 (sin.f64 ky) #s(literal -3602879701896397/72057594037927936 binary64)) (.f64 th (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (hypot.f64 kx (sin.f64 ky)))) (.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx)))))
(*.f64 ky (/.f64 (sin.f64 th) (hypot.f64 ky (sin.f64 kx))))
(if (<=.f64 (sin.f64 kx) #s(literal 6455624695217271/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky)) (*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
(if (<=.f64 (sin.f64 kx) #s(literal 6455624695217271/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) ky)) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sin.f64 kx))))
(if (<=.f64 (sin.f64 kx) #s(literal 6455624695217271/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(if (<=.f64 (sin.f64 kx) #s(literal 6455624695217271/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) ky)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(if (<=.f64 ky #s(literal 4040244775997481/9619630419041620901435312524449124464130795720328478190417063819395928166869436184427311097384012607618805661696 binary64)) (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) #s(literal 0 binary64)) ky)))
(if (<=.f64 ky #s(literal 4040244775997481/9619630419041620901435312524449124464130795720328478190417063819395928166869436184427311097384012607618805661696 binary64)) (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 ky (+.f64 (sin.f64 th) (sin.f64 th))) ky)))
(if (<=.f64 kx #s(literal 5325890373554249/322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672 binary64)) (sin.f64 th) (*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th)))
(if (<=.f64 kx #s(literal 5325890373554249/322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672 binary64)) (sin.f64 th) (*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(if (<=.f64 kx #s(literal 380000 binary64)) (sin.f64 th) (*.f64 (/.f64 ky (sin.f64 kx)) th))
(if (<=.f64 kx #s(literal 380000 binary64)) (sin.f64 th) (*.f64 th (/.f64 ky (sin.f64 kx))))
(if (<=.f64 kx #s(literal 180000 binary64)) (sin.f64 th) (*.f64 ky (/.f64 th (sin.f64 kx))))
(if (<=.f64 kx #s(literal 31499999999999998666211328 binary64)) (sin.f64 th) #s(literal 0 binary64))
(if (<=.f64 kx #s(literal 838083498911033/11972621413014756705924586149611790497021399392059392 binary64)) th #s(literal 0 binary64))
#s(literal 0 binary64)

soundness2.3s (18.9%)

Rules

8974×	`-lowering-.f32`
8974×	`-lowering-.f64`
7054×	`-lowering-.f32`
7054×	`-lowering-.f64`
6716×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	107
1	213	101
2	1558	101
0	8364	101
0	563	4385
1	1991	4081
0	8395	4081
0	13	16
1	19	11
2	27	11
3	28	11
0	28	11
0	660	6231
1	2346	5822
0	9038	5822
0	26	85
1	130	85
2	896	85
0	9428	85
0	632	5877
1	2186	5413
0	8133	5413
0	405	4445
1	1412	4111
2	5844	4111
0	8117	4111

Stop Event

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

Compiler

Compiled 1234 to 732 computations (40.7% saved)

preprocess162.0ms (1.3%)

Remove

(negabs th)

(negabs ky)

(abs kx)

Compiler

Compiled 786 to 306 computations (61.1% saved)

analyze254.0ms (2.1%)

sample1.7s (13.6%)

preprocess127.0ms (1%)

explain168.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize111.0ms (0.9%)

series39.0ms (0.3%)

rewrite224.0ms (1.8%)

simplify277.0ms (2.2%)

eval109.0ms (0.9%)

prune80.0ms (0.6%)

simplify395.0ms (3.2%)

localize187.0ms (1.5%)

series35.0ms (0.3%)

rewrite262.0ms (2.1%)

simplify480.0ms (3.9%)

eval131.0ms (1.1%)

prune184.0ms (1.5%)

simplify164.0ms (1.3%)

localize390.0ms (3.2%)

series23.0ms (0.2%)

rewrite337.0ms (2.7%)

simplify587.0ms (4.7%)

eval127.0ms (1%)

prune154.0ms (1.2%)

simplify347.0ms (2.8%)

localize145.0ms (1.2%)

series31.0ms (0.2%)

rewrite310.0ms (2.5%)

simplify379.0ms (3.1%)

eval201.0ms (1.6%)

prune242.0ms (2%)

regimes371.0ms (3%)

regimes208.0ms (1.7%)

regimes239.0ms (1.9%)

regimes32.0ms (0.3%)

regimes30.0ms (0.2%)

regimes29.0ms (0.2%)

regimes119.0ms (1%)

regimes75.0ms (0.6%)

regimes87.0ms (0.7%)

regimes15.0ms (0.1%)

regimes65.0ms (0.5%)

regimes42.0ms (0.3%)

regimes39.0ms (0.3%)

regimes4.0ms (0%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

bsearch35.0ms (0.3%)

bsearch33.0ms (0.3%)

bsearch32.0ms (0.3%)

bsearch36.0ms (0.3%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch22.0ms (0.2%)

bsearch16.0ms (0.1%)

bsearch31.0ms (0.2%)

bsearch29.0ms (0.2%)

bsearch33.0ms (0.3%)

bsearch20.0ms (0.2%)

simplify25.0ms (0.2%)

soundness2.3s (18.9%)

preprocess162.0ms (1.3%)

end0.0ms (0%)

Profiling