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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze256.0ms (1.8%)

Memory

27.7MiB live, 334.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	6
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	7
53.1%	53%	46.8%	0.1%	0%	0%	0%	8
60.9%	60.8%	39%	0.1%	0%	0%	0%	9
60.9%	60.8%	39%	0.1%	0%	0%	0%	10
64.8%	64.7%	35.1%	0.1%	0%	0%	0%	11
68.4%	68.3%	31.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.9s (12.9%)

Memory

74.5MiB live, 2 478.9MiB allocated

Samples

1.4s

8 256×

valid

Precisions

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

ival-sin: 654.0ms (57.2% of total)

ival-pow2: 236.0ms (20.7% of total)

ival-mult: 87.0ms (7.6% of total)

ival-sqrt: 61.0ms (5.3% of total)

ival-div: 54.0ms (4.7% of total)

ival-add: 41.0ms (3.6% of total)

ival-true: 7.0ms (0.6% of total)

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

Bogosity

explain264.0ms (1.8%)

Memory

50.8MiB live, 362.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
14	-	-	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	-	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	-	`(sin.f64 kx)`
0	-	-	`(sin.f64 th)`
0	-	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
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	-	-	`th`
0	-	-	`#s(literal 2 binary64)`
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	-	-	`(sin.f64 ky)`
0	-	-	`ky`
0	-	-	`kx`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	uflow-rescue	14	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	65
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	54
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	14

Confusion

	Predicted +	Predicted -
+	14	0
-	0	242

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	14	0	0
-	0	0	242

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	242
1	14

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

141.0ms

512×

valid

Compiler

Compiled 152 to 43 computations (71.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 121.0ms

ival-sin: 91.0ms (75.4% of total)

ival-pow2: 10.0ms (8.3% of total)

ival-div: 9.0ms (7.5% of total)

ival-sqrt: 4.0ms (3.3% of total)

ival-mult: 3.0ms (2.5% of total)

ival-add: 2.0ms (1.7% of total)

ival-true: 1.0ms (0.8% of total)

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

exact: 0.0ms (0% of total)

preprocess272.0ms (1.9%)

Memory

-23.2MiB live, 228.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	153
1	89	147
2	211	147
3	416	147
4	898	147
5	2624	147
6	5843	147
0	13	16
0	22	16
1	30	16
2	48	16
3	103	16
4	205	16
5	446	16
6	1158	16
7	2930	16
8	6994	16
0	8072	11

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.4%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify144.0ms (1%)

Memory

11.6MiB live, 203.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	5	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
0	22	66
1	30	66
2	48	66
3	103	66
4	205	66
5	446	66
6	1158	66
7	2930	66
8	6994	66
0	8072	51

Stop Event

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

Calls

Call 1

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

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

localize114.0ms (0.8%)

Memory

-19.1MiB live, 107.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
accuracy	0.21484375	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	0.2734375	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	3.368806192132544	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Samples

59.0ms

256×

valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-pow2: 24.0ms (49.3% of total)

ival-sin: 18.0ms (37% of total)

ival-div: 2.0ms (4.1% of total)

ival-mult: 2.0ms (4.1% of total)

ival-sqrt: 2.0ms (4.1% of total)

ival-add: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.3%)

Memory

28.2MiB live, 85.5MiB allocated

Counts

6 → 45

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	ky	@	0	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
5.0ms	th	@	-inf	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
4.0ms	kx	@	inf	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms	kx	@	0	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms	ky	@	inf	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))

simplify254.0ms (1.8%)

Memory

21.5MiB live, 272.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	1402
1	1134	1336
2	5236	1308
0	8406	1228

Stop Event

1×	iter limit
1×	node limit

Counts

45 → 44

Calls

Call 1

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

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

rewrite587.0ms (4.1%)

Memory

-59.0MiB live, 351.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
0	22	49
1	59	49
2	319	49
3	3129	49
0	8937	34

Stop Event

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

Counts

6 → 384

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (neg.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (/.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
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(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 kx) (+.f64 kx (PI.f64)))) (cos.f64 (+.f64 (neg.f64 kx) (+.f64 kx (PI.f64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 kx (PI.f64)) (neg.f64 kx))) (cos.f64 (+.f64 (+.f64 kx (PI.f64)) (neg.f64 kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 kx (PI.f64)) (+.f64 kx (PI.f64)))) (cos.f64 (+.f64 (+.f64 kx (PI.f64)) (+.f64 kx (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (.f64 (cos.f64 kx) (cos.f64 kx)))
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (-.f64 (.f64 (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -2 binary64))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(neg.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(fma.f64 #s(literal 2 binary64) (*.f64 (sinh.f64 (log.f64 (sin.f64 kx))) (cosh.f64 (log.f64 (sin.f64 kx)))) (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 kx) (cos.f64 kx)))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 kx)))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(fabs.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(fabs.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 kx))))
(exp.f64 (*.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64))) (sinh.f64 (.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64))))
(+.f64 (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))

eval160.0ms (1.1%)

Memory: 2.7MiB live, 190.6MiB allocated
Compiler: Compiled 12 601 to 2 762 computations (78.1% saved)

prune68.0ms (0.5%)

Memory

-15.8MiB live, 46.1MiB allocated

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	462	21	483
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	463	21	484

Accuracy

100.0%

Counts

484 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.1%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	93.8%	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
	76.3%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 2 binary64)) (sin.f64 ky))) (sin.f64 th))
▶	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	23.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (.f64 (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (sin.f64 th))
	83.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
	84.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
▶	44.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	86.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (cos.f64 kx) (cos.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	86.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	52.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	36.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
	31.4%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	39.5%	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	76.0%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	25.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	28.6%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	41.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	92.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky))))
▶	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 920 to 682 computations (25.9% saved)

simplify147.0ms (1%)

Memory

19.0MiB live, 149.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(sqrt.f64 (sin.f64 ky))
cost-diff	5	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.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) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	1	(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
cost-diff	0	(sin.f64 th)
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
cost-diff	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	295
0	71	285
1	119	285
2	256	285
3	587	285
4	1290	285
5	2900	285
6	6156	285
0	8190	280

Stop Event

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

Calls

Call 1

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

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

localize286.0ms (2%)

Memory

5.5MiB live, 385.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0546875	(sqrt.f64 (sin.f64 ky))
accuracy	0.18425751953688402	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
accuracy	0.1875	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.2421875	(*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
accuracy	0.12109375	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
accuracy	0.16015625	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	3.345368692132544	(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	10.570417350147578	(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
accuracy	0.12109375	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
accuracy	0.15625	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	3.345368692132544	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
accuracy	18.00314458267922	#s(approx (pow (sin ky) 2) (*.f64 ky ky))
accuracy	0.00390625	(sin.f64 th)
accuracy	28.296466903326905	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0.00390625	(sin.f64 th)
accuracy	0.015625	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.09375	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.12109375	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Samples

81.0ms	101×	0	valid
63.0ms	34×	2	valid
46.0ms	61×	1	valid
23.0ms	60×	0	invalid

Compiler

Compiled 323 to 32 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-cos: 46.0ms (32.7% of total)

ival-sin: 27.0ms (19.2% of total)

ival-mult: 18.0ms (12.8% of total)

ival-div: 10.0ms (7.1% of total)

adjust: 10.0ms (7.1% of total)

ival-pow2: 8.0ms (5.7% of total)

ival-sqrt: 8.0ms (5.7% of total)

ival-hypot: 6.0ms (4.3% of total)

ival-add: 4.0ms (2.8% of total)

ival-sub: 2.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series75.0ms (0.5%)

Memory

-16.5MiB live, 117.7MiB allocated

Counts

20 → 100

Calls

Call 1

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

Outputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(* (sqrt (/ 1 (sin ky))) (sin th))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (sin ky) 5))))) (* (sqrt (/ 1 (sin ky))) (sin th)))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))))) (sqrt (sin ky)))))))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 3))) (+ (* 2/3 (/ 1 (pow (sin ky) 5))) (/ 1 (pow (sin ky) 7))))))) (sqrt (sin ky)))) (* 1/2 (* (sqrt (sin ky)) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5))))))))))))
(/ (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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(sqrt ky)
(+ (sqrt ky) (* -1/12 (sqrt (pow ky 5))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* 1/240 (sqrt (pow ky 3))))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* (pow ky 2) (+ (* -1/288 (sqrt (/ 1 ky))) (* 1/240 (sqrt (/ 1 ky))))))))
(* (sqrt ky) (/ (sin th) (sin kx)))
(+ (* -1/2 (* (sqrt (pow ky 5)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (sqrt ky) (/ (sin th) (sin kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* 1/2 (* (sqrt (pow ky 3)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (pow ky 2) (+ (* -1/8 (* (sqrt (/ 1 ky)) (* (pow (sin kx) 3) (* (sin th) (pow (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) 2))))) (* 1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (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))))
(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
(/ (sin th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
(sqrt (sin ky))
(pow (sin ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* th (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))

Calls

9 calls:

Time	Variable		Point	Expression
19.0ms	kx	@	-inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
13.0ms	ky	@	-inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
10.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
6.0ms	ky	@	inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))
6.0ms	th	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))

simplify311.0ms (2.2%)

Memory

33.5MiB live, 280.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	666	4140
1	2457	3852
0	9402	3690

Stop Event

1×	iter limit
1×	node limit

Counts

100 → 98

Calls

Call 1

Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(* (sqrt (/ 1 (sin ky))) (sin th))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (sin ky) 5))))) (* (sqrt (/ 1 (sin ky))) (sin th)))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))))) (sqrt (sin ky)))))))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 3))) (+ (* 2/3 (/ 1 (pow (sin ky) 5))) (/ 1 (pow (sin ky) 7))))))) (sqrt (sin ky)))) (* 1/2 (* (sqrt (sin ky)) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5))))))))))))
(/ (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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(sqrt ky)
(+ (sqrt ky) (* -1/12 (sqrt (pow ky 5))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* 1/240 (sqrt (pow ky 3))))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* (pow ky 2) (+ (* -1/288 (sqrt (/ 1 ky))) (* 1/240 (sqrt (/ 1 ky))))))))
(* (sqrt ky) (/ (sin th) (sin kx)))
(+ (* -1/2 (* (sqrt (pow ky 5)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (sqrt ky) (/ (sin th) (sin kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* 1/2 (* (sqrt (pow ky 3)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (pow ky 2) (+ (* -1/8 (* (sqrt (/ 1 ky)) (* (pow (sin kx) 3) (* (sin th) (pow (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) 2))))) (* 1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (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))))
(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
(/ (sin th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
(sqrt (sin ky))
(pow (sin ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* th (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))

Outputs
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (/.f64 (.f64 (.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx)))) (.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
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(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (/.f64 (*.f64 kx kx) (sin.f64 ky)) #s(literal 1/2 binary64) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (.f64 kx kx)) #s(literal 1/2 binary64)) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
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(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))
(* (sqrt (/ 1 (sin ky))) (sin th))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (sin ky) 5))))) (* (sqrt (/ 1 (sin ky))) (sin th)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th) (.f64 (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 5 binary64)))) (.f64 (sin.f64 th) #s(literal -1/2 binary64)))))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))))) (sqrt (sin ky)))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 5 binary64)))) (sin.f64 th)) (.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 5 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (sin.f64 th)) (.f64 kx kx))))) (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th)))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 3))) (+ (* 2/3 (/ 1 (pow (sin ky) 5))) (/ 1 (pow (sin ky) 7))))))) (sqrt (sin ky)))) (* 1/2 (* (sqrt (sin ky)) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5))))))))))))
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(/ (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)))
(fma.f64 (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (/.f64 (sin.f64 th) (sin.f64 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)))
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(+ (* (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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(* (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt.f64 (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (fma.f64 #s(literal -1/5040 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (/.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (.f64 ky ky) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 (fma.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (.f64 ky ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (-.f64 (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) ky))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (-.f64 (.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))) (+.f64 (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)))) (.f64 ky ky) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) ky))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 #s(literal -1/6 binary64) (pow.f64 ky #s(literal 3 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 ky ky)) #s(literal 1/6 binary64)) (pow.f64 ky #s(literal 3 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 ky ky) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (pow.f64 ky #s(literal 3 binary64)) ky)
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal 1/2 binary64) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (.f64 ky ky)) #s(literal 1/2 binary64)) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (.f64 ky ky)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (.f64 ky ky) (sin.f64 kx))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th)) #s(literal 1/120 binary64) (fma.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (sin.f64 th) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/120 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (sin.f64 th)) (.f64 #s(literal -1/12 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (sin.f64 th)))) (fma.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))) (.f64 ky ky) (fma.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (sin.f64 th) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64))))) (.f64 ky ky) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal -1/6 binary64))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal 1/12 binary64) (fma.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal 1/120 binary64)))) (.f64 ky ky) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal -1/6 binary64)))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
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(sqrt ky)
(sqrt.f64 ky)
(+ (sqrt ky) (* -1/12 (sqrt (pow ky 5))))
(fma.f64 (sqrt.f64 (pow.f64 ky #s(literal 5 binary64))) #s(literal -1/12 binary64) (sqrt.f64 ky))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* 1/240 (sqrt (pow ky 3))))))
(fma.f64 (fma.f64 (sqrt.f64 (pow.f64 ky #s(literal 3 binary64))) #s(literal 1/240 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) #s(literal -1/12 binary64))) (pow.f64 ky #s(literal 3 binary64)) (sqrt.f64 ky))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* (pow ky 2) (+ (* -1/288 (sqrt (/ 1 ky))) (* 1/240 (sqrt (/ 1 ky))))))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) (.f64 #s(literal 1/1440 binary64) (.f64 ky ky)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) #s(literal -1/12 binary64))) (pow.f64 ky #s(literal 3 binary64)) (sqrt.f64 ky))
(* (sqrt ky) (/ (sin th) (sin kx)))
(*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(+ (* -1/2 (* (sqrt (pow ky 5)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (sqrt ky) (/ (sin th) (sin kx))))
(fma.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 ky #s(literal 5 binary64))) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* 1/2 (* (sqrt (pow ky 3)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)))) (.f64 (.f64 (sqrt.f64 (pow.f64 ky #s(literal 3 binary64))) (sin.f64 kx)) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/120 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 th))))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (pow ky 2) (+ (* -1/8 (* (sqrt (/ 1 ky)) (* (pow (sin kx) 3) (* (sin th) (pow (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) 2))))) (* 1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))))
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(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky))
(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal 1/3 binary64)) (.f64 ky ky)) #s(literal 1/2 binary64))) (.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 ky ky)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)))) (.f64 ky ky) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64))) (.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 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)))
(fma.f64 (.f64 ky ky) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (sin.f64 th) (sin.f64 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)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (sin.f64 kx)) (.f64 ky ky)))) (.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 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)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (sin.f64 kx)) (.f64 ky ky)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (sin.f64 kx)))) (.f64 ky ky) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(sqrt (sin ky))
(sqrt.f64 (sin.f64 ky))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 th (.f64 (sin.f64 ky) th)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 th (.f64 (sin.f64 ky) th)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 th (.f64 (sin.f64 ky) th)) (sin.f64 ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 th (.f64 (sin.f64 ky) th))))) (.f64 (.f64 th th) (*.f64 th th)))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (*.f64 th th) th) th)
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 th (.f64 (sin.f64 ky) th)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 th (.f64 (sin.f64 ky) th)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 th (.f64 (sin.f64 ky) th)) (sin.f64 ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 th (.f64 (sin.f64 ky) th))))) (.f64 (.f64 th th) (*.f64 th th)))) th)
(* th (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.f64 th th) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 (.f64 th th) (.f64 th th)))) th)
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
(* 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 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* 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 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* 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 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 (.f64 th th) (.f64 th th)))) th)

rewrite255.0ms (1.8%)

Memory

-7.4MiB live, 237.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	212
0	71	171
1	230	171
2	1412	171
0	8439	171

Stop Event

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

Counts

20 → 472

Calls

Call 1

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

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

eval182.0ms (1.3%)

Memory: 32.8MiB live, 288.3MiB allocated
Compiler: Compiled 21 265 to 3 085 computations (85.5% saved)

prune165.0ms (1.1%)

Memory

-40.1MiB live, 217.5MiB allocated

Pruning

31 alts after pruning (28 fresh and 3 done)

	Pruned	Kept	Total
New	721	23	744
Fresh	11	5	16
Picked	2	3	5
Done	0	0	0
Total	734	31	765

Accuracy

100.0%

Counts

765 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.1%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	43.4%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
	23.2%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))) (sin.f64 kx))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
▶	45.2%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	75.2%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
▶	42.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
✓	44.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	21.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	75.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	52.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	31.4%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	29.5%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	33.0%	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	52.4%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))))))
	32.1%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
	29.3%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))))
	35.0%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	70.8%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))))
	32.2%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
	28.2%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
	25.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	28.6%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	75.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 ky))) (sin.f64 th))
	24.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
✓	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	17.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
▶	17.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	34.0%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
	24.5%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
	27.5%	#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))

Compiler

Compiled 1 604 to 1 179 computations (26.5% saved)

simplify172.0ms (1.2%)

Memory

-5.6MiB live, 235.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	358
0	69	338
1	119	338
2	278	338
3	697	326
4	1887	326
5	3454	326
6	5482	326
0	8284	314

Stop Event

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

Calls

Call 1

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

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

localize130.0ms (0.9%)

Memory

54.5MiB live, 252.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
accuracy	0.21484375	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	3.368806192132544	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))
accuracy	33.205176390165065	#s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))
accuracy	0.11328125	(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy	0.14453125	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.16015625	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy	35.0487380731886	#s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy	0.00390625	(sin.f64 th)
accuracy	0.14453125	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
accuracy	0.16015625	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
accuracy	44.96308398871782	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))
accuracy	0.0703125	(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
accuracy	0.11328125	(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy	35.0487380731886	#s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy	42.93660357041274	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy	0.00390625	(sin.f64 th)
accuracy	0.03515625	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.21875	(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy	2.499648763602325	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Samples

106.0ms

256×

valid

Compiler

Compiled 298 to 31 computations (89.6% saved)

Precisions

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

ival-sin: 21.0ms (33.4% of total)

ival-mult: 16.0ms (25.4% of total)

const: 7.0ms (11.1% of total)

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

ival-add: 4.0ms (6.4% of total)

ival-hypot: 4.0ms (6.4% of total)

ival-pow2: 4.0ms (6.4% of total)

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

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

-2.0MiB live, 58.5MiB allocated

Counts

20 → 66

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	kx	@	0	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (+ (* (* ky ky) -1/3) 1) (* ky ky)) (* (/ (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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2))
3.0ms	ky	@	inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (+ (* (* ky ky) -1/3) 1) (* ky ky)) (* (/ (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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2))
2.0ms	ky	@	-inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (+ (* (* ky ky) -1/3) 1) (* ky ky)) (* (/ (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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2))
2.0ms	th	@	-inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (+ (* (* ky ky) -1/3) 1) (* ky ky)) (* (/ (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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2))
2.0ms	th	@	inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (+ (* (* ky ky) -1/3) 1) (* ky ky)) (* (/ (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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2))

simplify209.0ms (1.5%)

Memory

-15.9MiB live, 230.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	381	1660
1	1370	1566
2	6137	1534
0	8207	1439

Stop Event

1×	iter limit
1×	node limit

Counts

66 → 64

Calls

Call 1

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

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

rewrite244.0ms (1.7%)

Memory

-10.3MiB live, 255.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	255
0	69	235
1	227	235
2	1532	235
0	9657	235

Stop Event

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

Counts

20 → 324

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 th ky) (+.f64 ky th)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (-.f64 th ky) (+.f64 ky th)) #s(literal 2 binary64)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)))) (neg.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))) (neg.f64 (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(-.f64 (/.f64 (cos.f64 (-.f64 th ky)) (.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (cos.f64 (+.f64 ky th)) (.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(-.f64 (/.f64 (/.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (/.f64 (cos.f64 (+.f64 ky th)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th)))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky th)))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) #s(literal 2 binary64))
(-.f64 (/.f64 (cos.f64 (-.f64 ky th)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 ky th)) #s(literal 2 binary64)))
(-.f64 (/.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 ky th)) #s(literal 2 binary64)))
(sin.f64 th)
(*.f64 (neg.f64 (sqrt.f64 (sin.f64 ky))) (neg.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (fabs.f64 (sqrt.f64 (sin.f64 ky))) (fabs.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky))))
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
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(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal -2 binary64)))
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(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (sin.f64 kx) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (sin.f64 ky) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(exp.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
#s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))
(.f64 (neg.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky))) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 3/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (-.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (-.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)))))
(/.f64 (hypot.f64 (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 3/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(/.f64 (hypot.f64 (pow.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) #s(literal 3/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.f64 (fma.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (-.f64 #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky))))
(exp.f64 (.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky) ky)))) #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(*.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 kx))))
(*.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 kx)))
(*.f64 (sin.f64 kx) (sin.f64 kx))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sin.f64 kx)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) #s(literal 4 binary64))
(/.f64 (fabs.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))))) (fabs.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))))
(/.f64 (fabs.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(literal 2 binary64))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (neg.f64 kx) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (+.f64 (neg.f64 kx) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 kx (PI.f64)) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (+.f64 (+.f64 kx (PI.f64)) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 kx) (neg.f64 kx))) (cos.f64 (+.f64 (neg.f64 kx) (neg.f64 kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 kx) (+.f64 kx (PI.f64)))) (cos.f64 (+.f64 (neg.f64 kx) (+.f64 kx (PI.f64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 kx (PI.f64)) (neg.f64 kx))) (cos.f64 (+.f64 (+.f64 kx (PI.f64)) (neg.f64 kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 kx (PI.f64)) (+.f64 kx (PI.f64)))) (cos.f64 (+.f64 (+.f64 kx (PI.f64)) (+.f64 kx (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))
(neg.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (neg.f64 kx)))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))
(fabs.f64 (-.f64 (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (-.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(fabs.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))

eval107.0ms (0.7%)

Memory: -2.2MiB live, 186.1MiB allocated
Compiler: Compiled 19 249 to 2 277 computations (88.2% saved)

prune66.0ms (0.5%)

Memory

0.4MiB live, 121.9MiB allocated

Pruning

47 alts after pruning (42 fresh and 5 done)

	Pruned	Kept	Total
New	628	24	652
Fresh	5	18	23
Picked	2	3	5
Done	1	2	3
Total	636	47	683

Accuracy

100.0%

Counts

683 → 47

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.2%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))) (sin.f64 kx)))
✓	96.1%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	75.4%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
	75.2%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))))
	30.3%	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
▶	41.6%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	45.3%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	45.5%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	41.9%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	29.3%	(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	11.9%	(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	45.2%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	33.9%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	33.7%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	21.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	75.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	34.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
	52.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	25.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
✓	31.4%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	29.5%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	30.9%	(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	28.3%	(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	33.0%	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	52.4%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))))))
	32.1%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
	70.8%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))))
▶	32.2%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
	28.2%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
	31.4%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
	25.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	28.6%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
▶	75.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 ky))) (sin.f64 th))
	24.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
✓	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	17.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
	17.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
	17.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
	16.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
	9.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
▶	8.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
	8.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
	8.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
	34.0%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
▶	24.5%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
	27.5%	#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))

Compiler

Compiled 2 552 to 1 870 computations (26.7% saved)

simplify120.0ms (0.8%)

Memory

30.4MiB live, 215.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	519
0	112	514
1	186	514
2	388	514
3	814	510
4	2000	507
5	4767	507
0	8041	494

Stop Event

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

Calls

Call 1

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

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

localize450.0ms (3.1%)

Memory

-39.4MiB live, 671.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0859375	(.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)
accuracy	2.425430013602325	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	2.6467019807200685	(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))
accuracy	26.44127107549555	#s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th))
accuracy	0.07421875	(/.f64 #s(literal 1 binary64) (sin.f64 ky))
accuracy	0.18425751953688402	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
accuracy	0.26171875	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
accuracy	28.386971738727738	#s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th)))
accuracy	2.7624639776747664	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky))
accuracy	10.570417350147578	(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
accuracy	12.368415518033254	(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
accuracy	26.127242097228837	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
accuracy	0.12890625	(.f64 (.f64 th th) #s(literal -1/6 binary64))
accuracy	21.891271337439225	#s(approx (+ (* (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64)))
accuracy	26.484505026710686	#s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th))
accuracy	28.296466903326905	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
accuracy	0.1875	(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
accuracy	0.248378759768442	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 ky))
accuracy	3.4042768999423743	(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
accuracy	11.668771375633256	(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))

Samples

217.0ms	61×	2	valid
86.0ms	101×	0	valid
33.0ms	60×	0	invalid
31.0ms	13×	3	valid
19.0ms	21×	1	valid

Compiler

Compiled 415 to 57 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 304.0ms

ival-mult: 106.0ms (34.9% of total)

ival-cos: 70.0ms (23.1% of total)

ival-sin: 27.0ms (8.9% of total)

ival-pow2: 24.0ms (7.9% of total)

adjust: 20.0ms (6.6% of total)

ival-div: 16.0ms (5.3% of total)

ival-sqrt: 16.0ms (5.3% of total)

ival-add: 7.0ms (2.3% of total)

ival-sub: 6.0ms (2% of total)

ival-hypot: 6.0ms (2% of total)

const: 5.0ms (1.6% of total)

exact: 1.0ms (0.3% of total)

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

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

series132.0ms (0.9%)

Memory

56.2MiB live, 234.8MiB allocated

Counts

25 → 150

Calls

Call 1

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

Outputs
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(/ (* ky (sin th)) kx)
(/ (+ (* 1/6 (* (pow kx 2) (* ky (sin th)))) (* ky (sin th))) kx)
(/ (+ (* ky (sin th)) (* (pow kx 2) (+ (* 7/360 (* (pow kx 2) (* ky (sin th)))) (* 1/6 (* ky (sin th)))))) kx)
(/ (+ (* ky (sin th)) (* (pow kx 2) (+ (* 1/6 (* ky (sin th))) (* (pow kx 2) (+ (* 31/15120 (* (pow kx 2) (* ky (sin th)))) (* 7/360 (* ky (sin th)))))))) kx)
(/ 1 kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
(* (sqrt (/ 1 (sin ky))) (sin th))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (sin ky) 5))))) (* (sqrt (/ 1 (sin ky))) (sin th)))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))))) (sqrt (sin ky)))))))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 3))) (+ (* 2/3 (/ 1 (pow (sin ky) 5))) (/ 1 (pow (sin ky) 7))))))) (sqrt (sin ky)))) (* 1/2 (* (sqrt (sin ky)) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5))))))))))))
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(/ 1 (pow (sin ky) 2))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6)))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6))))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(- 1/2 (* 1/2 (cos (* -2 kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(* (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
(/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))
(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))))))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(sqrt ky)
(+ (sqrt ky) (* -1/12 (sqrt (pow ky 5))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* 1/240 (sqrt (pow ky 3))))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* (pow ky 2) (+ (* -1/288 (sqrt (/ 1 ky))) (* 1/240 (sqrt (/ 1 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))))
(* (sqrt ky) (/ (sin th) (sin kx)))
(+ (* -1/2 (* (sqrt (pow ky 5)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (sqrt ky) (/ (sin th) (sin kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* 1/2 (* (sqrt (pow ky 3)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (pow ky 2) (+ (* -1/8 (* (sqrt (/ 1 ky)) (* (pow (sin kx) 3) (* (sin th) (pow (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) 2))))) (* 1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))))
(* ky (* th (+ 1 (* -1/6 (pow th 2)))))
(* ky (+ (* -1/6 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2)))))) (* th (+ 1 (* -1/6 (pow th 2))))))
(* ky (+ (* th (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/6 (* th (+ 1 (* -1/6 (pow th 2))))) (* 1/120 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2))))))))))
(* ky (+ (* th (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/6 (* th (+ 1 (* -1/6 (pow th 2))))) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2)))))) (* 1/120 (* th (+ 1 (* -1/6 (pow th 2)))))))))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(* ky (+ 1 (* -1/6 (pow th 2))))
(* ky (+ 1 (+ (* -1/6 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))) (* -1/6 (pow th 2)))))
(* ky (+ 1 (+ (* -1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (+ 1 (* -1/6 (pow th 2)))) (* 1/120 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))))))))
(* ky (+ 1 (+ (* -1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))) (* 1/120 (+ 1 (* -1/6 (pow th 2)))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))
(+ (* -1 (/ (pow ky 2) (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(* (sqrt (/ 1 ky)) (sin th))
(/ (+ (* 1/12 (* (sqrt (pow ky 5)) (sin th))) (* (sqrt ky) (sin th))) ky)
(/ (+ (* (sqrt ky) (sin th)) (* (pow ky 3) (+ (* 7/720 (* (sqrt (pow ky 3)) (sin th))) (* 1/12 (* (sqrt (/ 1 ky)) (sin th)))))) ky)
(/ (+ (* (sqrt ky) (sin th)) (* (pow ky 3) (+ (* 1/12 (* (sqrt (/ 1 ky)) (sin th))) (* (pow ky 2) (+ (* -1/288 (* (sqrt (/ 1 ky)) (sin th))) (* 7/720 (* (sqrt (/ 1 ky)) (sin th)))))))) ky)
(/ 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)
(sqrt (sin ky))
(sin ky)
(* th (* (sin ky) (+ 1 (* -1/6 (pow th 2)))))
(* (sin ky) (sin th))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* ky th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(* th (+ (* -1/6 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))
(* th (+ (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(* th (+ (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))))
(* th (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(* th (sin ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(+ (sin ky) (* -1/6 (* (pow th 2) (sin ky))))
(* -1/6 (pow th 2))
(* th (sqrt (/ 1 (sin ky))))
(* th (+ (sqrt (/ 1 (sin ky))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (sin ky)))))))
(* th (+ (sqrt (/ 1 (sin ky))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (sin ky)))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (sin ky)))))))))
(* th (+ (sqrt (/ 1 (sin ky))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (sin ky)))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (sin ky))))) (* 1/120 (sqrt (/ 1 (sin ky))))))))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (* (pow th 3) (sin ky)))
(* (pow th 3) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* -1/6 (* (pow th 2) (sin ky)))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (+ (* -1 (/ (sin ky) (pow th 2))) (* 1/6 (sin ky)))))

Calls

9 calls:

Time	Variable		Point	Expression
40.0ms	ky	@	-inf	((- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (sin ky) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (* (+ (* (* th th) -1/6) 1) (sin ky)) th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* th th) -1/6) 1) (sin ky)) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (* th th) -1/6) (* (sqrt (/ 1 (sin ky))) (sin th)) (/ 1 (sin ky)))
18.0ms	ky	@	0	((- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (sin ky) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (* (+ (* (* th th) -1/6) 1) (sin ky)) th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* th th) -1/6) 1) (sin ky)) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (* th th) -1/6) (* (sqrt (/ 1 (sin ky))) (sin th)) (/ 1 (sin ky)))
17.0ms	th	@	inf	((- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (sin ky) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (* (+ (* (* th th) -1/6) 1) (sin ky)) th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* th th) -1/6) 1) (sin ky)) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (* th th) -1/6) (* (sqrt (/ 1 (sin ky))) (sin th)) (/ 1 (sin ky)))
14.0ms	ky	@	inf	((- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (sin ky) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (* (+ (* (* th th) -1/6) 1) (sin ky)) th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* th th) -1/6) 1) (sin ky)) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (* th th) -1/6) (* (sqrt (/ 1 (sin ky))) (sin th)) (/ 1 (sin ky)))
11.0ms	th	@	-inf	((- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sqrt (sin ky)) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))))) (sqrt (sin ky)) (sin ky) (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (* (* (+ (* (* th th) -1/6) 1) (sin ky)) th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* th th) -1/6) 1) (sin ky)) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (* th th) -1/6) (* (sqrt (/ 1 (sin ky))) (sin th)) (/ 1 (sin ky)))

simplify277.0ms (1.9%)

Memory

-15.4MiB live, 427.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	839	5392
1	3166	5062
0	8594	4833

Stop Event

1×	iter limit
1×	node limit

Counts

150 → 148

Calls

Call 1

Inputs
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(/ (* ky (sin th)) kx)
(/ (+ (* 1/6 (* (pow kx 2) (* ky (sin th)))) (* ky (sin th))) kx)
(/ (+ (* ky (sin th)) (* (pow kx 2) (+ (* 7/360 (* (pow kx 2) (* ky (sin th)))) (* 1/6 (* ky (sin th)))))) kx)
(/ (+ (* ky (sin th)) (* (pow kx 2) (+ (* 1/6 (* ky (sin th))) (* (pow kx 2) (+ (* 31/15120 (* (pow kx 2) (* ky (sin th)))) (* 7/360 (* ky (sin th)))))))) kx)
(/ 1 kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
(* (sqrt (/ 1 (sin ky))) (sin th))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (sin ky) 5))))) (* (sqrt (/ 1 (sin ky))) (sin th)))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))))) (sqrt (sin ky)))))))
(+ (* (sqrt (/ 1 (sin ky))) (sin th)) (* (pow kx 2) (+ (* -1/2 (* (sqrt (/ 1 (pow (sin ky) 5))) (sin th))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 3))) (+ (* 2/3 (/ 1 (pow (sin ky) 5))) (/ 1 (pow (sin ky) 7))))))) (sqrt (sin ky)))) (* 1/2 (* (sqrt (sin ky)) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 3))) (* 3/4 (/ 1 (pow (sin ky) 5))))))))))))
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(/ 1 (pow (sin ky) 2))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6)))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6))))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(- 1/2 (* 1/2 (cos (* -2 kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(* (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
(/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))
(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))))))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(sqrt ky)
(+ (sqrt ky) (* -1/12 (sqrt (pow ky 5))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* 1/240 (sqrt (pow ky 3))))))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* (pow ky 2) (+ (* -1/288 (sqrt (/ 1 ky))) (* 1/240 (sqrt (/ 1 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))))
(* (sqrt ky) (/ (sin th) (sin kx)))
(+ (* -1/2 (* (sqrt (pow ky 5)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (sqrt ky) (/ (sin th) (sin kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* 1/2 (* (sqrt (pow ky 3)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (pow ky 2) (+ (* -1/8 (* (sqrt (/ 1 ky)) (* (pow (sin kx) 3) (* (sin th) (pow (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) 2))))) (* 1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))))
(* ky (* th (+ 1 (* -1/6 (pow th 2)))))
(* ky (+ (* -1/6 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2)))))) (* th (+ 1 (* -1/6 (pow th 2))))))
(* ky (+ (* th (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/6 (* th (+ 1 (* -1/6 (pow th 2))))) (* 1/120 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2))))))))))
(* ky (+ (* th (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/6 (* th (+ 1 (* -1/6 (pow th 2))))) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2)))))) (* 1/120 (* th (+ 1 (* -1/6 (pow th 2)))))))))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(* ky (+ 1 (* -1/6 (pow th 2))))
(* ky (+ 1 (+ (* -1/6 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))) (* -1/6 (pow th 2)))))
(* ky (+ 1 (+ (* -1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (+ 1 (* -1/6 (pow th 2)))) (* 1/120 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))))))))
(* ky (+ 1 (+ (* -1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))) (* 1/120 (+ 1 (* -1/6 (pow th 2)))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))
(+ (* -1 (/ (pow ky 2) (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(* (sqrt (/ 1 ky)) (sin th))
(/ (+ (* 1/12 (* (sqrt (pow ky 5)) (sin th))) (* (sqrt ky) (sin th))) ky)
(/ (+ (* (sqrt ky) (sin th)) (* (pow ky 3) (+ (* 7/720 (* (sqrt (pow ky 3)) (sin th))) (* 1/12 (* (sqrt (/ 1 ky)) (sin th)))))) ky)
(/ (+ (* (sqrt ky) (sin th)) (* (pow ky 3) (+ (* 1/12 (* (sqrt (/ 1 ky)) (sin th))) (* (pow ky 2) (+ (* -1/288 (* (sqrt (/ 1 ky)) (sin th))) (* 7/720 (* (sqrt (/ 1 ky)) (sin th)))))))) ky)
(/ 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)
(sqrt (sin ky))
(sin ky)
(* th (* (sin ky) (+ 1 (* -1/6 (pow th 2)))))
(* (sin ky) (sin th))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* ky th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(* th (+ (* -1/6 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))
(* th (+ (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(* th (+ (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))))
(* th (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(* th (sin ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(+ (sin ky) (* -1/6 (* (pow th 2) (sin ky))))
(* -1/6 (pow th 2))
(* th (sqrt (/ 1 (sin ky))))
(* th (+ (sqrt (/ 1 (sin ky))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (sin ky)))))))
(* th (+ (sqrt (/ 1 (sin ky))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (sin ky)))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (sin ky)))))))))
(* th (+ (sqrt (/ 1 (sin ky))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (sin ky)))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (sin ky))))) (* 1/120 (sqrt (/ 1 (sin ky))))))))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (* (pow th 3) (sin ky)))
(* (pow th 3) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* -1/6 (* (pow th 2) (sin ky)))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (+ (* -1 (/ (sin ky) (pow th 2))) (* 1/6 (sin ky)))))

Outputs
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(+ (pow kx 2) (pow (sin ky) 2))
(fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(fma.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
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(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
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(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))))) (fma.f64 #s(literal -1/240 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (.f64 #s(literal -1/5040 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))))) (.f64 ky ky) (fma.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) (.f64 #s(literal 1/12 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))))))) (.f64 ky ky) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal -1/6 binary64)))) (.f64 ky ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) ky)
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sin.f64 th)) (fma.f64 (.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/5040 binary64) (/.f64 (.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (.f64 ky ky) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(sqrt ky)
(sqrt.f64 ky)
(+ (sqrt ky) (* -1/12 (sqrt (pow ky 5))))
(fma.f64 (sqrt.f64 (pow.f64 ky #s(literal 5 binary64))) #s(literal -1/12 binary64) (sqrt.f64 ky))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* 1/240 (sqrt (pow ky 3))))))
(fma.f64 (fma.f64 (sqrt.f64 (pow.f64 ky #s(literal 3 binary64))) #s(literal 1/240 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) #s(literal -1/12 binary64))) (pow.f64 ky #s(literal 3 binary64)) (sqrt.f64 ky))
(+ (sqrt ky) (* (pow ky 3) (+ (* -1/12 (sqrt (/ 1 ky))) (* (pow ky 2) (+ (* -1/288 (sqrt (/ 1 ky))) (* 1/240 (sqrt (/ 1 ky))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) #s(literal 1/1440 binary64)) (.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) #s(literal -1/12 binary64))) (pow.f64 ky #s(literal 3 binary64)) (sqrt.f64 ky))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 ky ky)) #s(literal 1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 ky ky) #s(literal 1/120 binary64)) (.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* (sqrt ky) (/ (sin th) (sin kx)))
(*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(+ (* -1/2 (* (sqrt (pow ky 5)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (sqrt ky) (/ (sin th) (sin kx))))
(fma.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 ky #s(literal 5 binary64))) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* 1/2 (* (sqrt (pow ky 3)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) (sin.f64 kx)) (.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))) (.f64 (.f64 (sqrt.f64 (pow.f64 ky #s(literal 3 binary64))) (sin.f64 kx)) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/120 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 th))))) (pow.f64 ky #s(literal 3 binary64)) (.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(+ (* (sqrt ky) (/ (sin th) (sin kx))) (* (pow ky 3) (+ (* -1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))))))) (* (pow ky 2) (+ (* -1/8 (* (sqrt (/ 1 ky)) (* (pow (sin kx) 3) (* (sin th) (pow (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) 2))))) (* 1/2 (* (sqrt (/ 1 ky)) (* (sin kx) (* (sin th) (- (+ (* 1/120 (/ 1 (pow (sin kx) 2))) (* 1/3 (/ 1 (pow (sin kx) 4)))) (* -1 (/ (+ (* 1/6 (/ 1 (pow (sin kx) 2))) (/ 1 (pow (sin kx) 4))) (pow (sin kx) 2)))))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) ky))) (.f64 (.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal 2 binary64)) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) ky))) (.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (+.f64 (+.f64 (/.f64 #s(literal 1/120 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) ky))) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (sin.f64 kx)))) (pow.f64 ky #s(literal 3 binary64)) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (* th (+ 1 (* -1/6 (pow th 2)))))
(.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)
(* ky (+ (* -1/6 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2)))))) (* th (+ 1 (* -1/6 (pow th 2))))))
(.f64 (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)
(* ky (+ (* th (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/6 (* th (+ 1 (* -1/6 (pow th 2))))) (* 1/120 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2))))))))))
(.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/120 binary64) (.f64 ky ky) #s(literal -1/6 binary64))) (.f64 ky ky) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)
(* ky (+ (* th (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/6 (* th (+ 1 (* -1/6 (pow th 2))))) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (* th (+ 1 (* -1/6 (pow th 2)))))) (* 1/120 (* th (+ 1 (* -1/6 (pow th 2)))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (.f64 (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) (fma.f64 #s(literal -1/5040 binary64) (.f64 ky ky) #s(literal 1/120 binary64))) (.f64 ky ky))) (.f64 ky ky) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
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(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
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(* ky (+ 1 (* -1/6 (pow th 2))))
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(* ky (+ 1 (+ (* -1/6 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))) (* -1/6 (pow th 2)))))
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(* ky (+ 1 (+ (* -1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (+ 1 (* -1/6 (pow th 2)))) (* 1/120 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))))))))
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(* ky (+ 1 (+ (* -1/6 (pow th 2)) (* (pow ky 2) (+ (* -1/6 (+ 1 (* -1/6 (pow th 2)))) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (+ 1 (* -1/6 (pow th 2))))) (* 1/120 (+ 1 (* -1/6 (pow th 2)))))))))))
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(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
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(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
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(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
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(/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
(+ (* -1 (/ (pow ky 2) (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
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(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
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(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
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(* (sqrt (/ 1 ky)) (sin th))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) ky)) (sin.f64 th))
(/ (+ (* 1/12 (* (sqrt (pow ky 5)) (sin th))) (* (sqrt ky) (sin th))) ky)
(/.f64 (*.f64 (sin.f64 th) (fma.f64 #s(literal 1/12 binary64) (sqrt.f64 (pow.f64 ky #s(literal 5 binary64))) (sqrt.f64 ky))) ky)
(/ (+ (* (sqrt ky) (sin th)) (* (pow ky 3) (+ (* 7/720 (* (sqrt (pow ky 3)) (sin th))) (* 1/12 (* (sqrt (/ 1 ky)) (sin th)))))) ky)
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(/ (+ (* (sqrt ky) (sin th)) (* (pow ky 3) (+ (* 1/12 (* (sqrt (/ 1 ky)) (sin th))) (* (pow ky 2) (+ (* -1/288 (* (sqrt (/ 1 ky)) (sin th))) (* 7/720 (* (sqrt (/ 1 ky)) (sin th)))))))) ky)
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(/ 1 ky)
(/.f64 #s(literal 1 binary64) ky)
(/ (+ 1 (* 1/6 (pow ky 2))) ky)
(/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* 7/360 (pow ky 2))))) ky)
(/.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 7/360 binary64) #s(literal 1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* (pow ky 2) (+ 7/360 (* 31/15120 (pow ky 2))))))) ky)
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(sqrt (sin ky))
(sqrt.f64 (sin.f64 ky))
(sin ky)
(sin.f64 ky)
(* th (* (sin ky) (+ 1 (* -1/6 (pow th 2)))))
(.f64 (.f64 th (sin.f64 ky)) (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
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(* (* 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
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th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* ky th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)
(* th (+ (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) ky) (.f64 #s(literal -1/6 binary64) ky))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) th)
(* th (+ (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* ky (pow th 2)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/120 binary64) ky (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) ky)))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) th)
(* th (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.f64 th th) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ (sin ky) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/6 binary64))) (.f64 th th) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (sin ky))
(*.f64 th (sin.f64 ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(.f64 (.f64 th (sin.f64 ky)) (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(.f64 (fma.f64 (.f64 (sin.f64 ky) (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.f64 th th) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 ky) (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 th th) (.f64 #s(literal -1/6 binary64) (sin.f64 ky))) (.f64 th th) (sin.f64 ky)) th)
(+ (sin ky) (* -1/6 (* (pow th 2) (sin ky))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))
(* -1/6 (pow th 2))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(* th (sqrt (/ 1 (sin ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th)
(* th (+ (sqrt (/ 1 (sin ky))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (sin ky)))))))
(.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) th)
(* th (+ (sqrt (/ 1 (sin ky))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (sin ky)))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (sin ky)))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) th)
(* th (+ (sqrt (/ 1 (sin ky))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (sin ky)))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (sin ky))))) (* 1/120 (sqrt (/ 1 (sin ky))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) #s(literal -1/6 binary64))) (.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) th)
(* -1/6 (pow th 3))
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))
(* -1/6 (* (pow th 3) (sin ky)))
(.f64 (.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)) (sin.f64 ky))
(* (pow th 3) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (/.f64 (sin.f64 ky) (.f64 th th))) (pow.f64 th #s(literal 3 binary64)))
(* -1/6 (* (pow th 2) (sin ky)))
(.f64 (.f64 (*.f64 th th) #s(literal -1/6 binary64)) (sin.f64 ky))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (/.f64 (sin.f64 ky) (.f64 th th))) (*.f64 th th))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (pow.f64 th #s(literal 3 binary64)))
(* -1 (* (pow th 3) (+ (* -1 (/ (sin ky) (pow th 2))) (* 1/6 (sin ky)))))
(.f64 (neg.f64 (pow.f64 th #s(literal 3 binary64))) (fma.f64 #s(literal 1/6 binary64) (sin.f64 ky) (/.f64 (neg.f64 (sin.f64 ky)) (.f64 th th))))

rewrite421.0ms (2.9%)

Memory

-31.2MiB live, 486.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	417
0	113	385
1	348	316
2	2268	309
0	9253	309

Stop Event

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

Counts

25 → 383

Calls

Call 1

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

Outputs
(/.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64))))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (+.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64)))))))
(/.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (neg.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (neg.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (fma.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal -2 binary64) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (*.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))
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(/.f64 (.f64 (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/216 binary64) #s(literal 1 binary64)) (.f64 th (sin.f64 ky))) (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 th th) #s(literal -1/6 binary64)))))
(/.f64 (neg.f64 (neg.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))) (sin.f64 ky))))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))) (sin.f64 ky)))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))) (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (neg.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))) (sin.f64 ky)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))) (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (sin th) (sin ky)) (.f64 (.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))) (sin.f64 ky)))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))
(.f64 (sin.f64 ky) (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/36 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (-.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/216 binary64) #s(literal 1 binary64)) (sin.f64 ky)) (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 th th) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (sin.f64 ky) (-.f64 (.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/36 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (sin.f64 ky) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/216 binary64) #s(literal 1 binary64))) (fma.f64 (pow.f64 th #s(literal 4 binary64)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 th th) #s(literal -1/6 binary64)))))
(fma.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) (sin.f64 ky) (*.f64 #s(literal 1 binary64) (sin.f64 ky)))
(fma.f64 #s(literal 1 binary64) (sin.f64 ky) (.f64 (.f64 (*.f64 th th) #s(literal -1/6 binary64)) (sin.f64 ky)))
(fma.f64 (sin.f64 ky) (.f64 (.f64 th th) #s(literal -1/6 binary64)) (*.f64 (sin.f64 ky) #s(literal 1 binary64)))
(fma.f64 (sin.f64 ky) #s(literal 1 binary64) (.f64 (sin.f64 ky) (.f64 (*.f64 th th) #s(literal -1/6 binary64))))
(+.f64 (.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) (sin.f64 ky)) (.f64 #s(literal 1 binary64) (sin.f64 ky)))
(+.f64 (.f64 #s(literal 1 binary64) (sin.f64 ky)) (.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) (sin.f64 ky)))
(+.f64 (.f64 (sin.f64 ky) (.f64 (.f64 th th) #s(literal -1/6 binary64))) (.f64 (sin.f64 ky) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 ky) #s(literal 1 binary64)) (.f64 (sin.f64 ky) (.f64 (.f64 th th) #s(literal -1/6 binary64))))
(*.f64 (neg.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal -1 binary64))) (hypot.f64 (sin.f64 ky) (cos.f64 kx)))
(.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (hypot.f64 (sin.f64 ky) (cos.f64 kx)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)))
(fabs.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(exp.f64 (/.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(.f64 (pow.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal -1 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))
(.f64 (pow.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64)) (fma.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (*.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))))
(exp.f64 (fma.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64) (*.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)))))
(.f64 (.f64 #s(literal -1/6 binary64) (neg.f64 th)) (neg.f64 th))
(.f64 (.f64 #s(literal -1/6 binary64) th) th)
(.f64 (neg.f64 th) (.f64 (neg.f64 th) #s(literal -1/6 binary64)))
(.f64 (.f64 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 #s(literal -1/6 binary64) (.f64 (*.f64 th th) #s(literal 1 binary64)))
(.f64 #s(literal -1/6 binary64) (.f64 th th))
(.f64 th (.f64 (*.f64 #s(literal -1/6 binary64) th) #s(literal 1 binary64)))
(.f64 th (.f64 #s(literal -1/6 binary64) th))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 th th) #s(literal -1/6 binary64)))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) (sin.f64 th))
(*.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (sqrt.f64 (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (neg.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal -2 binary64))
(pow.f64 (sin.f64 ky) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(neg.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)))
(sqrt.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (sin.f64 ky))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 (sin.f64 ky))) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 (sin.f64 ky))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (neg.f64 (log.f64 (sin.f64 ky))))
(+.f64 (cosh.f64 (neg.f64 (log.f64 (sin.f64 ky)))) (sinh.f64 (neg.f64 (log.f64 (sin.f64 ky)))))

eval202.0ms (1.4%)

Memory: 57.8MiB live, 306.5MiB allocated
Compiler: Compiled 32 935 to 3 984 computations (87.9% saved)

prune245.0ms (1.7%)

Memory

-40.5MiB live, 219.1MiB allocated

Pruning

70 alts after pruning (62 fresh and 8 done)

	Pruned	Kept	Total
New	658	33	691
Fresh	8	29	37
Picked	2	3	5
Done	0	5	5
Total	668	70	738

Accuracy

100.0%

Counts

738 → 70

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.2%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))) (sin.f64 kx)))
✓	96.1%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	75.4%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
	75.2%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))))
	30.3%	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
	20.2%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
	19.4%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	41.9%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	19.6%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	29.3%	(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	11.9%	(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	45.2%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	33.9%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	33.7%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	75.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	34.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
	52.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	31.4%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	29.5%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	30.9%	(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	28.3%	(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	33.0%	(.f64 (sqrt.f64 (/.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	25.0%	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
	32.1%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
	32.3%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
	70.8%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))))
✓	32.2%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
	17.7%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
	28.2%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
	16.9%	(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
	31.4%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
	25.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	28.6%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	75.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
	24.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
	42.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
	26.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
	26.9%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
	29.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
	32.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
	27.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
✓	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	17.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
	17.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
	17.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
	9.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
	9.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
✓	8.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
	8.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
	8.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
	8.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
	16.0%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
	27.5%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
	28.6%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
	28.6%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
	34.0%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
	11.2%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
✓	24.5%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
	24.4%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
	9.5%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))
	15.0%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
	16.8%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
	14.7%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
	16.9%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
	14.7%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
	18.8%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
	18.8%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
	11.5%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
	11.3%	#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))

Compiler

Compiled 5 546 to 2 294 computations (58.6% saved)

regimes473.0ms (3.3%)

Memory

25.6MiB live, 415.2MiB allocated

Counts

102 → 1

Calls

Call 1

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

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

Calls

9 calls:

100.0ms	kx
82.0ms	ky
67.0ms	(sin.f64 ky)
64.0ms	(sin.f64 kx)
41.0ms	(sin.f64 th)

Results

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

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes392.0ms (2.7%)

Memory

-36.1MiB live, 469.1MiB allocated

Counts

80 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))))

Outputs

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

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

Calls

9 calls:

71.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
58.0ms	th
48.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
46.0ms	(sin.f64 kx)
45.0ms	kx

Results

Accuracy	Segments	Branch
86.7%	3	`(sin.f64 th)`
93.9%	3	`(sin.f64 kx)`
93.9%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
95.4%	3	`(sin.f64 ky)`
97.0%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
81.7%	4	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
93.9%	2	`kx`
95.3%	2	`ky`
86.7%	2	`th`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes25.0ms (0.2%)

Memory

50.2MiB live, 50.2MiB allocated

Counts

76 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))

Outputs

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

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

Calls

1 calls:

20.0ms

ky

Results

Accuracy	Segments	Branch
95.3%	2	`ky`

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes280.0ms (1.9%)

Memory

-14.7MiB live, 367.8MiB allocated

Counts

75 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))

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

Calls

8 calls:

48.0ms	(sin.f64 ky)
45.0ms	kx
41.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
40.0ms	ky
34.0ms	(sin.f64 kx)

Results

Accuracy	Segments	Branch
73.1%	3	`(sin.f64 th)`
73.0%	3	`th`
74.5%	4	`(sin.f64 kx)`
74.3%	3	`(sin.f64 ky)`
83.9%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
74.6%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
72.7%	2	`kx`
74.2%	2	`ky`

Compiler

Compiled 26 to 38 computations (-46.2% saved)

regimes42.0ms (0.3%)

Memory

11.0MiB live, 71.7MiB allocated

Counts

74 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))

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

Calls

1 calls:

38.0ms

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

Results

Accuracy	Segments	Branch
83.9%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes64.0ms (0.4%)

Memory

6.2MiB live, 73.7MiB allocated

Counts

73 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))))

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

Calls

1 calls:

60.0ms

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

Results

Accuracy	Segments	Branch
83.8%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes64.0ms (0.4%)

Memory

8.0MiB live, 66.6MiB allocated

Counts

70 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) ky)))

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

Calls

1 calls:

60.0ms

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

Results

Accuracy	Segments	Branch
83.5%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes37.0ms (0.3%)

Memory

6.5MiB live, 64.9MiB allocated

Counts

66 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

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

Calls

1 calls:

33.0ms

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

Results

Accuracy	Segments	Branch
83.5%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes75.0ms (0.5%)

Memory

-54.3MiB live, 77.8MiB allocated

Counts

64 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))

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

Calls

1 calls:

42.0ms

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

Results

Accuracy	Segments	Branch
83.3%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes94.0ms (0.7%)

Memory

40.1MiB live, 166.2MiB allocated

Counts

62 → 4

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))

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

Calls

3 calls:

50.0ms

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

24.0ms

ky

16.0ms

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

Results

Accuracy	Segments	Branch
67.1%	2	`ky`
59.8%	4	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
77.0%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 30 to 27 computations (10% saved)

regimes271.0ms (1.9%)

Memory

-20.6MiB live, 293.5MiB allocated

Counts

60 → 4

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

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

Calls

8 calls:

59.0ms	(sin.f64 ky)
58.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
42.0ms	ky
34.0ms	th
28.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
65.1%	3	`ky`
61.0%	5	`(sin.f64 kx)`
60.4%	3	`th`
62.4%	4	`(sin.f64 th)`
59.9%	4	`kx`
67.9%	4	`(sin.f64 ky)`
61.1%	4	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
69.9%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 26 to 38 computations (-46.2% saved)

regimes18.0ms (0.1%)

Memory

42.8MiB live, 42.8MiB allocated

Counts

59 → 4

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))

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

Calls

1 calls:

14.0ms

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

Results

Accuracy	Segments	Branch
69.5%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes138.0ms (1%)

Memory

-37.1MiB live, 114.7MiB allocated

Counts

57 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (* (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))

Outputs

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

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

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

Calls

5 calls:

68.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
21.0ms	(sin.f64 th)
16.0ms	(sin.f64 ky)
15.0ms	ky
15.0ms	th

Results

Accuracy	Segments	Branch
40.3%	3	`th`
44.0%	5	`(sin.f64 th)`
58.3%	3	`ky`
59.7%	3	`(sin.f64 ky)`
56.4%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 25 computations (-31.6% saved)

regimes510.0ms (3.5%)

Memory

-38.7MiB live, 150.8MiB allocated

Counts

54 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 #s(approx (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (-.f64 (fma.f64 ky ky #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))

Outputs

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

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

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

Calls

4 calls:

382.0ms	(sin.f64 ky)
40.0ms	kx
14.0ms	ky
13.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
52.1%	4	`ky`
58.3%	3	`kx`
58.3%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
53.5%	4	`(sin.f64 ky)`

Compiler

Compiled 8 to 16 computations (-100% saved)

regimes56.0ms (0.4%)

Memory

4.4MiB live, 66.3MiB allocated

Counts

48 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 ky) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))))

Outputs

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

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

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

Calls

2 calls:

41.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
13.0ms	kx

Results

Accuracy	Segments	Branch
58.3%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
58.3%	3	`kx`

Compiler

Compiled 5 to 9 computations (-80% saved)

regimes68.0ms (0.5%)

Memory

34.9MiB live, 96.1MiB allocated

Counts

44 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
(*.f64 (/.f64 (fabs.f64 (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (- (+ ( (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 #s(approx ( (+ (* (* th th) -1/6) 1) (sin ky)) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Outputs

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

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

Calls

4 calls:

33.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
11.0ms	kx
11.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
10.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
56.4%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
46.9%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
53.6%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
53.6%	3	`kx`

Compiler

Compiled 34 to 33 computations (2.9% saved)

regimes81.0ms (0.6%)

Memory

-19.9MiB live, 41.6MiB allocated

Counts

36 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (sin.f64 th) ky)))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) #s(approx (* (sqrt (/ 1 (sin ky))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky))) th))))
(.f64 (sqrt.f64 (sin.f64 ky)) #s(approx ( (sqrt (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))) (*.f64 (sqrt.f64 #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (fma.f64 kx #s(literal -2 binary64) (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 ( (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64)))))))) (.f64 (sin.f64 th) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (sin.f64 th)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) (.f64 (sin.f64 th) ky)))

Outputs

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

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

Calls

2 calls:

70.0ms	(sin.f64 kx)
9.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
52.9%	3	`(sin.f64 kx)`
54.8%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes8.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Counts

23 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))

Outputs

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

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

Calls

1 calls:

6.0ms

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

Results

Accuracy	Segments	Branch
54.8%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes66.0ms (0.5%)

Memory

12.3MiB live, 84.1MiB allocated

Counts

21 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (.f64 th (.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) kx)) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (- 1/2 ( (cos (* -2 kx)) 1/2)))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 kx kx)))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 th ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (/ 1 (- 1/2 (* (cos (* -2 kx)) 1/2)))) (* (sin th) ky)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) ky) ky)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 2/45 binary64) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1/2 ( (cos (* -2 kx)) 1/2)) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx)) #s(literal 1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))))) (*.f64 (sin.f64 th) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))) th)))

Outputs

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

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

Calls

6 calls:

35.0ms	kx
6.0ms	ky
6.0ms	(sin.f64 kx)
6.0ms	(sin.f64 ky)
6.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
42.0%	2	`ky`
41.9%	2	`(sin.f64 ky)`
37.8%	2	`(sin.f64 kx)`
38.5%	2	`kx`
39.2%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
45.6%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 23 to 31 computations (-34.8% saved)

regimes51.0ms (0.4%)

Memory

-37.9MiB live, 81.8MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Calls

9 calls:

16.0ms	(sin.f64 kx)
10.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
3.0ms	(sin.f64 th)
3.0ms	ky
3.0ms	th

Results

Accuracy	Segments	Branch
35.0%	2	`(sin.f64 kx)`
32.9%	1	`kx`
35.3%	2	`th`
35.0%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
32.9%	1	`(sin.f64 th)`
32.9%	1	`(sin.f64 ky)`
32.9%	1	`ky`
38.0%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
37.7%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes58.0ms (0.4%)

Memory

27.6MiB live, 85.3MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

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

Calls

9 calls:

34.0ms	kx
3.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
3.0ms	(sin.f64 th)
3.0ms	(sin.f64 ky)
3.0ms	ky

Results

Accuracy	Segments	Branch
20.0%	2	`ky`
20.2%	2	`(sin.f64 ky)`
20.5%	2	`kx`
20.0%	2	`(sin.f64 th)`
20.1%	2	`(sin.f64 kx)`
21.1%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
19.8%	2	`th`
23.3%	2	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
22.7%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes3.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
22.7%	2	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes55.0ms (0.4%)

Memory

-18.3MiB live, 42.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

9 calls:

42.0ms	(sin.f64 kx)
2.0ms	kx
1.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
1.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
1.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
8.8%	1	`th`
8.8%	1	`(sin.f64 th)`
8.8%	1	`ky`
8.8%	1	`(sin.f64 kx)`
8.8%	1	`(sin.f64 ky)`
8.8%	1	`kx`
8.8%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
8.8%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
8.8%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch48.0ms (0.3%)

Memory

4.0MiB live, 56.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	0.00116387722251395	0.042789021568725466

Samples

14.0ms

112×

valid

Compiler

Compiled 474 to 375 computations (20.9% saved)

Precisions

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

ival-sin: 6.0ms (54.4% of total)

ival-pow2: 2.0ms (18.1% 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)

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

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

bsearch2.0ms (0%)

Memory

8.6MiB live, 8.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
2.0ms	0.00116387722251395	0.042789021568725466

Compiler

Compiled 348 to 291 computations (16.4% saved)

bsearch1.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.052552234601788976	0.06416321552782207
0.0ms	-0.10759713226591501	2.912981389329033e-304
0.0ms	-0.9999999980049327	-0.9995416155462576

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.052552234601788976	0.06416321552782207
0.0ms	-0.10759713226591501	2.912981389329033e-304
0.0ms	-0.9999999980049327	-0.9995416155462576

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch2.0ms (0%)

Memory

7.0MiB live, 7.0MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.052552234601788976	0.06416321552782207
0.0ms	-0.10759713226591501	2.912981389329033e-304
0.0ms	-1.0	-0.9999999980049327

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.052552234601788976	0.06416321552782207
0.0ms	-0.10759713226591501	2.912981389329033e-304
0.0ms	-1.0	-0.9999999980049327

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

6.7MiB live, 6.7MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.052552234601788976	0.06416321552782207
0.0ms	-0.10759713226591501	2.912981389329033e-304
0.0ms	-1.0	-0.9999999980049327

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.06416321552782207	0.07410197222375689
0.0ms	-0.10759713226591501	2.912981389329033e-304
0.0ms	-1.0	-0.9999999980049327

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.06416321552782207	0.07410197222375689
0.0ms	-0.10759713226591501	2.912981389329033e-304

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.06416321552782207	0.07410197222375689
0.0ms	-0.10759713226591501	2.912981389329033e-304

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch12.0ms (0.1%)

Memory

-51.2MiB live, 4.4MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	0.9971533403956437	0.9999999999960912
0.0ms	0.06416321552782207	0.07410197222375689
0.0ms	-0.10759713226591501	2.912981389329033e-304

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.9026888755685803e-5	0.0011638769597473104
0.0ms	5.163763896029663e-152	3.723446806792453e-149

Compiler

Compiled 18 to 18 computations (0% saved)

bsearch41.0ms (0.3%)

Memory

29.6MiB live, 87.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
22.0ms	5.366433956894376e-7	1.4238312560242447e-6
16.0ms	1.0954603967196069e-144	9.689587979174931e-144

Samples

30.0ms

176×

valid

Compiler

Compiled 734 to 562 computations (23.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-div: 9.0ms (36.6% of total)

ival-sin: 9.0ms (36.6% of total)

ival-pow2: 3.0ms (12.2% of total)

ival-add: 1.0ms (4.1% of total)

ival-mult: 1.0ms (4.1% of total)

ival-sqrt: 1.0ms (4.1% of total)

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

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

bsearch2.0ms (0%)

Memory

7.2MiB live, 7.2MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	5.366433956894376e-7	1.4238312560242447e-6
1.0ms	1.0954603967196069e-144	9.689587979174931e-144

Compiler

Compiled 624 to 497 computations (20.4% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.07410197222375689	0.34324308115369717

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.052552234601788976	0.06416321552782207

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.052552234601788976	0.06416321552782207

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.9215513995271276e-5	0.052552234601788976

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch65.0ms (0.5%)

Memory

-55.3MiB live, 27.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
64.0ms	4.258207817413463e-34	5.452074870968397e-33

Samples

6.0ms

96×

valid

Compiler

Compiled 343 to 271 computations (21% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sin: 2.0ms (64.4% of total)

ival-mult: 1.0ms (32.2% of total)

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

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

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.4e-323	6.71085881223867e-305

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.4e-323	6.71085881223867e-305

Compiler

Compiled 19 to 19 computations (0% saved)

simplify101.0ms (0.7%)

Memory

42.7MiB live, 108.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	251	2388
1	342	2388
2	548	2388
3	983	2388
4	1854	2388
5	4009	2388

Stop Event

1×	node limit

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 ky #s(literal 7194230188746725/4611686018427387904 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th)))
(if (<=.f64 ky #s(literal 7194230188746725/4611686018427387904 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1125449546879887/1125899906842624 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1125449546879887/1125899906842624 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
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(if (<=.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 5/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (-.f64 (.f64 (.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th))))
(if (<=.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 5/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 ky #s(literal 7194230188746725/4611686018427387904 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th)))
(if (<=.f64 ky #s(literal 7194230188746725/4611686018427387904 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)) #s(literal -1 binary64))) (sin.f64 ky))) (sin.f64 th)))
(if (<=.f64 ky #s(literal 7194230188746725/4611686018427387904 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1125449546879887/1125899906842624 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1125449546879887/1125899906842624 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (pow.f64 (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal -1 binary64))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1125449546879887/1125899906842624 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1125449546879887/1125899906842624 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (pow.f64 (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (.f64 (cos.f64 (.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal -1 binary64))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1080863910568919/18014398509481984 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4494592428115755/4503599627370496 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 #s(literal -1/6 binary64) th) th)) th)))

soundness2.7s (18.7%)

Memory

-84.5MiB live, 2 651.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
0	22	49
1	59	49
2	319	49
3	3129	49
0	8937	34
0	41	255
0	69	235
1	227	235
2	1532	235
0	9657	235
0	381	1660
1	1370	1566
2	6137	1534
0	8207	1439
0	839	5392
1	3166	5062
0	8594	4833
0	317	1402
1	1134	1336
2	5236	1308
0	8406	1228
0	666	4140
1	2457	3852
0	9402	3690
0	41	212
0	71	171
1	230	171
2	1412	171
0	8439	171
0	73	417
0	113	385
1	348	316
2	2268	309
0	9253	309

Stop Event

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

Compiler

Compiled 4 652 to 1 718 computations (63.1% saved)

preprocess228.0ms (1.6%)

Memory

17.9MiB live, 404.5MiB allocated

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 4 880 to 582 computations (88.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated