Toniolo and Linder, Equation (3b), real

Time bar (total: 14.2s)

analyze240.0ms (1.7%)

Memory
-14.9MiB live, 429.0MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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)

sample1.5s (10.8%)

Memory
63.5MiB live, 2 418.2MiB allocated
Samples
1.2s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.0s
ival-sin: 582.0ms (57.7% of total)
ival-pow2: 180.0ms (17.8% of total)
ival-sqrt: 74.0ms (7.3% of total)
ival-mult: 62.0ms (6.1% of total)
ival-div: 61.0ms (6% of total)
ival-add: 39.0ms (3.9% of total)
ival-true: 7.0ms (0.7% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

preprocess75.0ms (0.5%)

Memory
-4.4MiB live, 34.2MiB allocated
Algorithm
1×egg-herbie
Rules
390×unsub-neg
362×times-frac
340×associate-*l*
334×associate-*r*
280×distribute-lft-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045153
1101147
2211147
3383147
4831147
51949147
62504147
72781147
82893147
92943147
102958147
112958147
01316
02216
12816
23216
33316
03311
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Symmetry

(abs kx)

(negabs th)

(negabs ky)

explain249.0ms (1.7%)

Memory
19.4MiB live, 293.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
170-5(8.461069676430521e-159 5.12259304438532e-171 9.86727708530919e+139)(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
00-0-(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
00-0-(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
00-0-(sin.f64 kx)
00-0-(sin.f64 th)
00-0-(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
00-0-(/.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)))))
00-0-th
00-0-#s(literal 2 binary64)
00-0-(*.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))
00-0-(sin.f64 ky)
00-0-ky
00-0-kx
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))uflow-rescue120
↳(pow.f64 (sin.f64 kx) #s(literal 2 binary64))underflow67
↳(pow.f64 (sin.f64 ky) #s(literal 2 binary64))underflow62
↳(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))underflow12
Confusion
Predicted +Predicted -
+125
-0239
Precision
1.0
Recall
0.7058823529411765
Confusion?
Predicted +Predicted MaybePredicted -
+1205
-00239
Precision?
1.0
Recall?
0.7058823529411765
Freqs
test
numberfreq
0244
112
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
141.0ms512×0valid
Compiler

Compiled 174 to 56 computations (67.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 113.0ms
ival-sin: 87.0ms (77.2% of total)
ival-pow2: 10.0ms (8.9% of total)
ival-div: 6.0ms (5.3% of total)
ival-sqrt: 4.0ms (3.6% of total)
ival-mult: 3.0ms (2.7% of total)
ival-add: 2.0ms (1.8% of total)
ival-true: 1.0ms (0.9% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Compiler

Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶94.6%
(*.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 19 to 13 computations (31.6% saved)

simplify7.0ms (0%)

Memory
-29.7MiB live, 9.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(/.f64 (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-diff0
(*.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-diff7296
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
Rules
16×lower-*.f32
14×lower-*.f64
6×lift-sin.f64
6×*-commutative
6×lower-sin.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01366
02266
12866
23266
33366
03351
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 (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 ky) (sin.f64 kx)))
(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 ky) (sin.f64 kx))
(+.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

localize65.0ms (0.5%)

Memory
-14.7MiB live, 93.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓accuracy99.6%
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓accuracy99.6%
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
✓accuracy94.9%
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
Samples
50.0ms256×0valid
Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-sin: 18.0ms (45% of total)
ival-mult: 13.0ms (32.5% of total)
ival-pow2: 5.0ms (12.5% of total)
ival-div: 2.0ms (5% of total)
ival-sqrt: 2.0ms (5% of total)
ival-add: 1.0ms (2.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series30.0ms (0.2%)

Memory
9.2MiB live, 47.6MiB allocated
Counts
6 → 120
Calls
Call 1
Inputs
#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (sin ky) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky)))))) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky)))))) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sin kx) (taylor 0 ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx)))) (taylor 0 ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin 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)))))) (taylor 0 ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sin 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)))))) (taylor 0 ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf ky) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) (taylor 0 ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3)))) (taylor 0 ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
Calls

30 calls:

TimeVariablePointExpression
3.0ms
kx
@0
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
3.0ms
kx
@0
(pow (sin kx) 2)
3.0ms
ky
@inf
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
2.0ms
ky
@0
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
2.0ms
th
@inf
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

simplify391.0ms (2.7%)

Memory
25.0MiB live, 526.7MiB allocated
Algorithm
1×egg-herbie
Rules
14 278×lower-fma.f64
14 278×lower-fma.f32
6 260×lower-*.f64
6 260×lower-*.f32
5 352×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03172263
110112214
238602122
378042122
081071974
Stop Event
1×iter limit
1×node limit
Counts
120 → 119
Calls
Call 1
Inputs
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
Outputs
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 kx (*.f64 kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 (*.f64 kx kx) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx (*.f64 kx (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (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 ky ky) (fma.f64 ky (/.f64 (*.f64 ky (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (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 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 ky ky) (-.f64 (/.f64 #s(literal 2/45 binary64) (sin.f64 kx)) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx)))) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 ky (/.f64 (*.f64 ky (*.f64 #s(literal -1/2 binary64) (sin.f64 th))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 ky (/.f64 (*.f64 ky (*.f64 #s(literal -1/2 binary64) (sin.f64 th))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (fma.f64 (*.f64 ky ky) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (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)))))) (sin.f64 th) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 ky (/.f64 (*.f64 ky (*.f64 #s(literal -1/2 binary64) (sin.f64 th))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (fma.f64 (*.f64 ky ky) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (*.f64 (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)))))) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (sin.f64 kx) (fma.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))) #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)))) #s(literal -1/12 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/5040 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (sin.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 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 kx kx) #s(literal -1/2 binary64)) (*.f64 (sin.f64 th) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) th))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal -1/6 binary64) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (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 (fma.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (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 (/.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 (*.f64 ky ky)) (/.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 (*.f64 ky ky) (*.f64 (+.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 kx) (fma.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))) #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)))) #s(literal -1/12 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 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (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 -1/6 binary64) (sin.f64 kx))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) ky) (/.f64 ky (sin.f64 kx)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 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 kx kx) (fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 (*.f64 (*.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))))) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1 binary64))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (*.f64 ky ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (*.f64 ky ky) (*.f64 (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) ky) ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(*.f64 kx (fma.f64 (*.f64 kx (*.f64 kx #s(literal -1/3 binary64))) kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(*.f64 (*.f64 (fma.f64 (*.f64 kx kx) (fma.f64 kx (*.f64 kx #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) kx) kx)
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(*.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))

rewrite330.0ms (2.3%)

Memory
-15.8MiB live, 415.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 346×lower-fma.f64
4 346×lower-fma.f32
3 626×lower-*.f32
3 624×lower-*.f64
2 248×lower-pow.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01349
02249
16249
233849
3290249
0828434
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
6 → 294
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #s(literal 1/4 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #s(literal -1/2 binary64))))
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (sin.f64 kx))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #s(literal 1 binary64))
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(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))))
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)))
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (sin.f64 ky)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(literal 1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sqrt.f64 (sin.f64 ky))) (sqrt.f64 (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))
(*.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 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sin.f64 ky)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sin.f64 ky))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (sin.f64 ky))) #s(literal 2 binary64)))
(exp.f64 (neg.f64 (neg.f64 (log.f64 (sin.f64 ky)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 ky)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(sin.f64 ky)
(neg.f64 (neg.f64 (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(pow.f64 (sin.f64 ky) #s(literal 1 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (sin.f64 ky))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sin.f64 ky)))
(*.f64 (sin.f64 ky) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 ky))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 ky)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (sqrt.f64 (sin.f64 ky))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 kx))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 kx))))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (+.f64 kx kx)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 kx))))
(*.f64 (sin.f64 kx) (sin.f64 kx))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 kx)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 kx)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 ky))))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (+.f64 ky ky)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 ky ky))))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))))
(*.f64 (sin.f64 ky) (sin.f64 ky))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal 1 binary64))
(*.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 ky)))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) #s(literal 1/2 binary64))

eval61.0ms (0.4%)

Memory
0.8MiB live, 114.8MiB allocated
Compiler

Compiled 12 851 to 1 670 computations (87% saved)

prune97.0ms (0.7%)

Memory
22.5MiB live, 187.1MiB allocated
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New42226448
Fresh000
Picked101
Done000
Total42326449
Accuracy
100.0%
Counts
449 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.2%
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
77.1%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
77.3%
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky)))
76.5%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
76.4%
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))) #s(literal -1 binary64)))
77.2%
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky))
▶99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
77.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
47.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
87.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
52.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 (*.f64 kx kx) (fma.f64 kx (*.f64 kx #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶52.9%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
29.8%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx)))) (sin.f64 th))
32.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
77.2%
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky)) (sin.f64 th))
53.2%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))) (sin.f64 th))
▶77.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
▶77.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
23.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
28.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
24.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
27.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
91.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
45.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) th)))
24.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 ky (fma.f64 ky (/.f64 (*.f64 ky (*.f64 #s(literal -1/2 binary64) (sin.f64 th))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))))))
▶30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Compiler

Compiled 1 202 to 808 computations (32.8% saved)

simplify96.0ms (0.7%)

Memory
2.8MiB live, 78.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓cost-diff192
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
✓cost-diff384
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
✓cost-diff1088
(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
✓cost-diff0
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
✓cost-diff128
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓cost-diff192
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
✓cost-diff384
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓cost-diff0
(sin.f64 th)
✓cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
✓cost-diff0
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Rules
1 494×lower-fma.f32
1 492×lower-fma.f64
562×lower-*.f32
548×lower-*.f64
412×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045404
077395
1106395
2142387
3207371
4286371
5349371
6456371
7612371
8824359
91118359
101645359
111980359
122094359
132104359
142112359
152118359
02118355
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 th)
th
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 ky)
ky
(sin.f64 th)
th
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
ky
(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(sin.f64 th)
th
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(sin.f64 ky)
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.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 #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) (sin.f64 th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 th)
th
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 ky ky))))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 ky)
ky
(sin.f64 th)
th
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 ky ky)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 ky ky))))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 ky ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 ky ky)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 ky ky))))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
ky
(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(sin.f64 ky)

localize312.0ms (2.2%)

Memory
0.2MiB live, 427.1MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
✓accuracy96.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
✓accuracy93.5%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
✓accuracy76.7%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓accuracy96.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
✓accuracy93.5%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
✓accuracy76.7%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓accuracy99.7%
(/.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)))))
✓accuracy99.6%
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓accuracy94.9%
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓accuracy49.8%
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
✓accuracy100.0%
(sin.f64 th)
✓accuracy30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
✓accuracy100.0%
(sin.f64 kx)
✓accuracy99.9%
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓accuracy99.8%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓accuracy99.7%
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Samples
117.0ms100×2valid
78.0ms86×1valid
30.0ms70×0valid
Compiler

Compiled 412 to 38 computations (90.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 174.0ms
ival-mult: 37.0ms (21.3% of total)
ival-cos: 36.0ms (20.7% of total)
ival-sin: 24.0ms (13.8% of total)
ival-hypot: 20.0ms (11.5% of total)
adjust: 16.0ms (9.2% of total)
ival-div: 13.0ms (7.5% of total)
ival-add: 10.0ms (5.8% of total)
ival-pow2: 8.0ms (4.6% of total)
ival-sqrt: 7.0ms (4% of total)
ival-sub: 2.0ms (1.2% of total)
exact: 1.0ms (0.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series47.0ms (0.3%)

Memory
10.8MiB live, 87.8MiB allocated
Counts
20 → 456
Calls
Call 1
Inputs
#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (patch (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.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)) #<representation binary64>) () ())
#s(alt (/.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))))) (patch (/.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))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) (patch (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))) (patch (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt (sin.f64 kx) (patch (sin.f64 kx) #<representation binary64>) () ())
#s(alt #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (patch #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())
Outputs
#s(alt (/ (* ky (sin th)) (sin kx)) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (sin th) (taylor 0 kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (taylor 0 kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))) (taylor 0 kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf kx) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor 0 th) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 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))))))) (taylor 0 th) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))))) (taylor 0 th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))))))) (taylor 0 th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor -inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor -inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor -inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (taylor -inf th) (#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) #<representation binary64>) () ())) ())
Calls

114 calls:

TimeVariablePointExpression
6.0ms
ky
@0
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))))
2.0ms
th
@inf
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))))
1.0ms
kx
@0
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))))
1.0ms
kx
@inf
(+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))
1.0ms
th
@0
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))))

simplify527.0ms (3.7%)

Memory
-17.8MiB live, 686.0MiB allocated
Algorithm
1×egg-herbie
Rules
12 454×lower-fma.f64
12 454×lower-fma.f32
9 136×lower-*.f64
9 136×lower-*.f32
4 032×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066811658
1217111177
2792411151
0812110384
Stop Event
1×iter limit
1×node limit
Counts
456 → 453
Calls
Call 1
Inputs
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow kx 2)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
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(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
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(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 2 (- 1 (cos (* 2 kx))))
(+ (* -4 (/ (pow ky 2) (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 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))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* 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) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* ky (sin th))
(* 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))))))))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* -1/2 (* (pow kx 2) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (* 1/2 (* (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* -2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (pow ky 2) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
Outputs
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (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) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal 1/12 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 th) (sin.f64 kx))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1/120 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) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) #s(literal 1/2 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 kx) (sin.f64 th))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (fma.f64 (sin.f64 kx) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) #s(literal -1/12 binary64)) (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/240 binary64) (/.f64 (*.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #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) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (sin.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 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (*.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))) (sin.f64 th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 th (fma.f64 th (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 th (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 th th) (*.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (*.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (neg.f64 ky) (/.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 (-.f64 (*.f64 (*.f64 ky ky) (fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky (*.f64 ky ky)) (/.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 (-.f64 (fma.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 (*.f64 ky ky) (fma.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 (sin.f64 kx) #s(literal -1/2 binary64)) (-.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (neg.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky (*.f64 ky ky)) (/.f64 ky (sin.f64 kx)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 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 kx kx) (fma.f64 kx (*.f64 kx (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1 binary64))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (*.f64 ky ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (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 ky ky) (fma.f64 (*.f64 ky ky) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (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 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (/.f64 (*.f64 ky ky) (sin.f64 kx))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 kx (*.f64 kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 (*.f64 kx kx) (sin.f64 ky))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (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) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal 1/12 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 th) (sin.f64 kx))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1/120 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) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) #s(literal 1/2 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 kx) (sin.f64 th))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (fma.f64 (sin.f64 kx) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) #s(literal -1/12 binary64)) (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/240 binary64) (/.f64 (*.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #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) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (sin.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 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (*.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))) (sin.f64 th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 th (fma.f64 th (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 th (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 th th) (*.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(fma.f64 (fma.f64 th (*.f64 th (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (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) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal 1/12 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 th) (sin.f64 kx))) (/.f64 (*.f64 (sin.f64 th) #s(literal 1/120 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) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) #s(literal 1/2 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 kx) (sin.f64 th))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (fma.f64 (sin.f64 kx) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))) #s(literal -1/12 binary64)) (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/240 binary64) (/.f64 (*.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #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) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (sin.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 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (*.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))) (sin.f64 th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 th (fma.f64 th (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 th (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 th th) (*.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (*.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (neg.f64 ky) (/.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 (-.f64 (*.f64 (*.f64 ky ky) (fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (+.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky (*.f64 ky ky)) (/.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 (-.f64 (fma.f64 (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)) (fma.f64 (*.f64 ky ky) (fma.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 (sin.f64 kx) #s(literal -1/2 binary64)) (-.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal -1/12 binary64))) (+.f64 (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (fma.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (neg.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky (*.f64 ky ky)) (/.f64 ky (sin.f64 kx)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 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 kx kx) (fma.f64 kx (*.f64 kx (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1 binary64))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 kx (*.f64 kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 (*.f64 kx kx) (sin.f64 ky))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (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 ky ky) (fma.f64 (*.f64 ky ky) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (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 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (/.f64 (*.f64 ky ky) (sin.f64 kx))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow kx 2)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))))
(fma.f64 kx (*.f64 kx (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 kx (*.f64 kx #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(* 1/2 (- 1 (cos (* 2 kx))))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (*.f64 ky ky))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
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(/ 2 (- 1 (cos (* 2 kx))))
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64)))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(*.f64 ky (fma.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal -1/6 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal 1/120 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal -1/6 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal 1/120 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/12 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/60 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/5040 binary64))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/3 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 th (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 th th) (*.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
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kx
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64)))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(*.f64 ky (fma.f64 (sin.f64 th) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal -1/6 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal 1/120 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal -1/6 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (sin.f64 th) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal 1/120 binary64)) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/12 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/60 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/5040 binary64))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/3 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 th (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 th th) (*.f64 th th)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))

rewrite114.0ms (0.8%)

Memory
-3.5MiB live, 191.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
780×lower-fma.f32
778×lower-fma.f64
716×lower-*.f32
702×lower-*.f64
672×lower-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
045238
077227
1277200
01983200
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
20 → 331
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 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(sin.f64 kx)
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) (*.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (sin.f64 ky) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky))))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)) #s(literal -1 binary64))
(*.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky))
(exp.f64 (*.f64 (log.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(sin.f64 ky)
(/.f64 (sin.f64 ky) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
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(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 ky ky)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 (+.f64 ky ky)) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))))
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(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 (+.f64 ky ky))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (neg.f64 (cos.f64 (+.f64 ky ky))) (neg.f64 (cos.f64 (+.f64 ky ky)))) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 ky ky)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 (+.f64 ky ky))) (neg.f64 (cos.f64 (+.f64 ky ky))))) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 ky ky)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 ky ky)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))))
(*.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 ky ky)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)))
(/.f64 (sin.f64 th) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (*.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 th))) (*.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 (*.f64 (neg.f64 (sin.f64 th)) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th)))) (*.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (neg.f64 (sin.f64 th))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))
(/.f64 (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th)))) #s(literal 2 binary64))
(/.f64 (*.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))
(/.f64 (*.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 th) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky))
(*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (sin.f64 ky))
(*.f64 (/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal -1 binary64)) (neg.f64 (sin.f64 ky)))

eval151.0ms (1.1%)

Memory
12.4MiB live, 279.6MiB allocated
Compiler

Compiled 33 735 to 2 190 computations (93.5% saved)

prune271.0ms (1.9%)

Memory
4.3MiB live, 399.9MiB allocated
Pruning

48 alts after pruning (46 fresh and 2 done)

PrunedKeptTotal
New1 144331 177
Fresh81321
Picked325
Done000
Total1 155481 203
Accuracy
100.0%
Counts
1 203 → 48
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.2%
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
11.6%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
77.1%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
77.3%
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky)))
43.4%
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
76.4%
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))) #s(literal -1 binary64)))
11.8%
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky))
77.2%
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky))
✓99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
50.0%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
57.8%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
52.2%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
▶77.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
▶87.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
43.4%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
28.1%
(*.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))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
29.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
32.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
43.4%
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
77.2%
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky)) (sin.f64 th))
53.2%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))) (sin.f64 th))
77.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
37.9%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
37.5%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
38.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
38.2%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
84.2%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))))
35.6%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
30.7%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
32.9%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
28.8%
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
77.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
39.8%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
40.3%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
37.5%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
30.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
32.9%
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
▶43.4%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
24.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
28.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
27.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
30.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
45.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) th)))
✓30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
14.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
▶14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
28.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
▶39.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
Compiler

Compiled 2 298 to 1 519 computations (33.9% saved)

simplify311.0ms (2.2%)

Memory
-8.0MiB live, 305.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
✓cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
✓cost-diff128
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓cost-diff384
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
✓cost-diff0
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
✓cost-diff0
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
✓cost-diff192
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
✓cost-diff384
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
✓cost-diff0
(sin.f64 th)
✓cost-diff0
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
✓cost-diff0
(*.f64 th (*.f64 th #s(literal -1/6 binary64)))
✓cost-diff0
(fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)
✓cost-diff0
#s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))
✓cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓cost-diff128
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
Rules
6 518×lower-fma.f32
6 506×lower-fma.f64
3 812×lower-*.f32
3 786×lower-*.f64
1 524×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077604
0127598
1195598
2315593
3606571
41228571
51562571
62271569
74100569
86386559
97166559
107980559
08042539
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (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 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))
(fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)
th
(*.f64 th (*.f64 th #s(literal -1/6 binary64)))
(*.f64 th #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(sin.f64 ky)
ky
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 th)
th
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
th
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(cos.f64 (*.f64 kx #s(literal -2 binary64)))
(*.f64 kx #s(literal -2 binary64))
kx
#s(literal -2 binary64)
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 ky #s(literal -2 binary64)))
(*.f64 ky #s(literal -2 binary64))
ky
(*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))
(fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 th #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(sin.f64 ky)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(sin.f64 ky)
ky
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
#s(literal 1 binary64)
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
(sin.f64 th)
th
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (+.f64 #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 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(sqrt.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
(fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))
(fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)
th
(*.f64 th (*.f64 th #s(literal -1/6 binary64)))
(*.f64 th #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 ky)
ky
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 th)
th
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (cos.f64 (*.f64 ky #s(literal -2 binary64)))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (cos.f64 (*.f64 ky #s(literal -2 binary64)))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
th
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (cos.f64 (*.f64 ky #s(literal -2 binary64)))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (cos.f64 (*.f64 ky #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (cos.f64 (*.f64 ky #s(literal -2 binary64)))))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) (cos.f64 (*.f64 ky #s(literal -2 binary64)))) #s(literal 1 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(cos.f64 (*.f64 kx #s(literal -2 binary64)))
(*.f64 kx #s(literal -2 binary64))
kx
#s(literal -2 binary64)
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 ky #s(literal -2 binary64)))
(*.f64 ky #s(literal -2 binary64))
ky
(*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))
(*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 th #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(sin.f64 ky)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))))
(sin.f64 ky)
ky
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
#s(literal 1 binary64)
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
(*.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
(sin.f64 th)
th

localize547.0ms (3.8%)

Memory
27.8MiB live, 862.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
✓accuracy94.9%
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
✓accuracy76.7%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓accuracy92.2%
(*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
✓accuracy76.7%
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))
✓accuracy50.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
✓accuracy99.6%
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
✓accuracy94.9%
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓accuracy76.7%
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
✓accuracy49.8%
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
✓accuracy99.8%
(*.f64 th (*.f64 th #s(literal -1/6 binary64)))
✓accuracy99.5%
(*.f64 th #s(literal -1/6 binary64))
✓accuracy50.2%
#s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))
✓accuracy30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
✓accuracy99.7%
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓accuracy99.6%
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓accuracy94.9%
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓accuracy79.9%
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
Samples
208.0ms113×2valid
122.0ms73×1valid
47.0ms70×0valid
Compiler

Compiled 560 to 68 computations (87.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 288.0ms
ival-cos: 82.0ms (28.4% of total)
ival-mult: 54.0ms (18.7% of total)
adjust: 34.0ms (11.8% of total)
ival-sqrt: 26.0ms (9% of total)
ival-sin: 25.0ms (8.7% of total)
ival-add: 22.0ms (7.6% of total)
ival-div: 17.0ms (5.9% of total)
ival-pow2: 12.0ms (4.2% of total)
ival-sub: 7.0ms (2.4% of total)
const: 5.0ms (1.7% of total)
exact: 1.0ms (0.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series172.0ms (1.2%)

Memory
8.6MiB live, 279.5MiB allocated
Counts
30 → 636
Calls
Call 1
Inputs
#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))) #<representation binary64>) () ())
#s(alt #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (patch #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) #<representation binary64>) () ())
#s(alt (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th) (patch (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th) #<representation binary64>) () ())
#s(alt (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (patch (*.f64 th (*.f64 th #s(literal -1/6 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (patch (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))) (patch #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))) #<representation binary64>) () ())
#s(alt (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))) (patch (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) (patch (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (patch (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 th #s(literal -1/6 binary64)) (patch (*.f64 th #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (patch #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #<representation binary64>) () ())
#s(alt (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (patch (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())
Outputs
#s(alt (pow kx 2) (taylor 0 kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (taylor 0 kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (taylor 0 kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) (taylor 0 kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (* 2 kx)))) (taylor inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (* 2 kx)))) (taylor inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (* 2 kx)))) (taylor inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (* 2 kx)))) (taylor inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (neg (* -2 kx))))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (neg (* -2 kx))))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (neg (* -2 kx))))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (- 1/2 (* 1/2 (cos (neg (* -2 kx))))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (patch (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) #<representation binary64>) () ())) ())
#s(alt (* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 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)))))))))))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 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))))))))))))))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* 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))))))))))))))))))))) (taylor 0 ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* th (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor 0 th) (#s(alt (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))) (taylor 0 th) (#s(alt (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
Calls

159 calls:

TimeVariablePointExpression
33.0ms
kx
@inf
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))))
20.0ms
kx
@inf
(sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))
15.0ms
ky
@0
(* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th))
12.0ms
th
@0
(* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky))))
3.0ms
ky
@0
(* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky))))

simplify544.0ms (3.8%)

Memory
-14.5MiB live, 817.4MiB allocated
Algorithm
1×egg-herbie
Rules
9 084×lower-fma.f64
9 084×lower-fma.f32
7 494×lower-+.f64
7 494×lower-+.f32
6 932×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0111517975
1379117082
0825815995
Stop Event
1×iter limit
1×node limit
Counts
636 → 632
Calls
Call 1
Inputs
(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))))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
(- 1/2 (* 1/2 (cos (neg (* -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)))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(* (* 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))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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) (sin th)) (sqrt (/ 1 (- (+ 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)))))))
(* 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))))))))))))))))))))
(* (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) (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) (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)))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (- (+ 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) (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 (neg (* -2 kx))))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 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 ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (pow th 3))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* th (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
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(sin th)
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(sin th)
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(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (- 1 (cos (* -2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))))) (* 4 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* -2 kx))))))
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
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(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
(* -1/6 (* (* (pow th 3) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx))))))))))
(* (pow th 3) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
(* (pow th 3) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
(* (pow th 3) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
(* -1/6 (* (* (pow th 3) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx))))))))))
(* -1 (* (pow th 3) (+ (* -1 (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* 1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))))
(* -1 (* (pow th 3) (+ (* -1 (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* 1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))))
(* -1 (* (pow th 3) (+ (* -1 (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* 1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* -2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2)))))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))) (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* -2 ky))))))))
(+ (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* -2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* th (* (sin ky) (* (+ 1 (* -1/6 (pow th 2))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* -2 ky))))))))))
(+ (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* -2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* th (* (sin ky) (* (+ 1 (* -1/6 (pow th 2))) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* -2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 4))))))))) (sqrt (+ 1/2 (* -1/2 (cos (* -2 ky))))))) (* 1/2 (* (* th (* (sin ky) (* (+ 1 (* -1/6 (pow th 2))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* -2 ky))))))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* ky (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2)))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* ky (+ (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (* -1/6 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))))))))
(* ky (+ (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (+ (* -1/6 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (+ (* 1/3 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (* 1/2 (* (/ (* th (* (+ 1 (* -1/6 (pow th 2))) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* -2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* -2 kx))))))))))))))
(* ky (+ (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (+ (* -1/6 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (+ (* 1/3 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (+ (* 1/2 (* (/ (* th (* (+ 1 (* -1/6 (pow th 2))) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* -2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* th (* (+ 1 (* -1/6 (pow th 2))) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* -2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* -2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (- 1 (cos (* -2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* -2 kx)))))) (+ (* -1/12 (* (/ (* th (* (+ 1 (* -1/6 (pow th 2))) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* -2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* -2 kx)))))) (+ (* -1/60 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (* -1/5040 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))))))))))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow kx 2)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 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))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
(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)))))))))))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 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))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(* -1/6 th)
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (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))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (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))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(+ 1/2 (* -1/2 (cos (* -2 ky))))
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(sin ky)
(+ (sin ky) (* -1/6 (* (pow th 2) (sin ky))))
(+ (sin ky) (* -1/6 (* (pow th 2) (sin ky))))
(+ (sin ky) (* -1/6 (* (pow th 2) (sin ky))))
(* -1/6 (* (pow th 2) (sin ky)))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* (pow th 2) (+ (* -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))))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* (pow th 2) (+ (* -1/6 (sin ky)) (/ (sin ky) (pow th 2))))
(* 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)))))))))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* (sin ky) (+ 1 (* -1/6 (pow th 2))))
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
Outputs
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
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(- 1/2 (* 1/2 (cos (* 2 kx))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))
(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
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(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
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(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
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(- 1/2 (* 1/2 (cos (neg (* -2 kx)))))
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(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(* 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))))))))))))
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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)))))))))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal -1/6 binary64) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #s(literal 1/120 binary64) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 4 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))))))) (*.f64 #s(literal -1/12 binary64) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64))))))) (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 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 th) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (*.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 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))))))) (*.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 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64))))))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (*.f64 kx kx) (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 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* 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)))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))
(* 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 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (*.f64 #s(literal 1/120 binary64) (*.f64 (sin.f64 ky) (*.f64 th th))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))))
(* 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 th (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))))))) (*.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (sin.f64 ky) (*.f64 th th)) (*.f64 #s(literal 1/120 binary64) (sin.f64 ky)))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(* 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)))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(* 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)))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) #s(literal 1/12 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #s(literal 1/120 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #s(literal -1/6 binary64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(* 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 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #s(literal 1/120 binary64) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 4 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64)))))) (*.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) #s(literal -1/240 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #s(literal -1/5040 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) #s(literal 1/12 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))))))))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64))) #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #s(literal -1/6 binary64)))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 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 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #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 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1 binary64))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (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))))) (fma.f64 #s(literal 1/12 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal 1/120 binary64) (sin.f64 th)) (sin.f64 kx)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/120 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (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))))) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (fma.f64 #s(literal -1/12 binary64) (*.f64 (*.f64 (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))))) (fma.f64 #s(literal -1/240 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (*.f64 kx kx) (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 kx kx) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (sin.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 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th)) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))))))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (*.f64 #s(literal 1/120 binary64) (*.f64 (sin.f64 ky) (*.f64 th th))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (sin.f64 ky) (*.f64 th th)) (*.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (*.f64 th (*.f64 th th)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal -1/6 binary64)))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (*.f64 th (*.f64 th th)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal -1/6 binary64)))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (*.f64 th (*.f64 th th)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal -1/6 binary64)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (*.f64 th (*.f64 th th)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 th th)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (*.f64 th (*.f64 th th)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 th th)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (*.f64 th (*.f64 th th)) (neg.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 th th)))))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(* -1/6 (pow th 2))
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (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))))) (fma.f64 #s(literal 1/12 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal 1/120 binary64) (sin.f64 th)) (sin.f64 kx)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/120 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (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))))) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (fma.f64 #s(literal -1/12 binary64) (*.f64 (*.f64 (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))))) (fma.f64 #s(literal -1/240 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (*.f64 #s(literal 1/120 binary64) (*.f64 (sin.f64 ky) (*.f64 th th))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (sin.f64 ky) (*.f64 th th)) (*.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (+.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 kx kx) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* th (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))
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(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
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(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
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(+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
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th
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(/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal -4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 th) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal -4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/12 binary64) (/.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal -4 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (*.f64 #s(literal -1/60 binary64) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (*.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))))) (fma.f64 (*.f64 #s(literal -2 binary64) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (*.f64 #s(literal 1/120 binary64) (*.f64 (sin.f64 ky) (*.f64 th th))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (sin.f64 ky) (*.f64 th th)) (*.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
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(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
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(* -1/6 (* (* (pow th 3) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx))))))))))
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(* (pow th 3) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))) (* (/ (sin ky) (pow th 2)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))))
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(+ (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* -2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* th (* (sin ky) (* (+ 1 (* -1/6 (pow th 2))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* -2 ky))))))))))
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(+ (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* -2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* th (* (sin ky) (* (+ 1 (* -1/6 (pow th 2))) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* -2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 4))))))))) (sqrt (+ 1/2 (* -1/2 (cos (* -2 ky))))))) (* 1/2 (* (* th (* (sin ky) (* (+ 1 (* -1/6 (pow th 2))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* -2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* -2 ky))))))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* th (* (sin ky) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* -2 ky))) (* 1/2 (- 1 (cos (* -2 kx)))))))))
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(* (* ky (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2)))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* ky (+ (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (* -1/6 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))))))))
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(* ky (+ (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (+ (* -1/6 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* th (* (sqrt 2) (+ 1 (* -1/6 (pow th 2))))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (+ (* 1/3 (* (/ (* th (+ 1 (* -1/6 (pow th 2)))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* -2 kx))) 3))))) (* 1/2 (* (/ (* th (* (+ 1 (* -1/6 (pow th 2))) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* -2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* -2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* -2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* -2 kx))))))))))))))
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(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))
(pow ky 2)
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(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
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(+ 1/2 (* -1/2 (cos (* 2 ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
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(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
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(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (sin.f64 ky) (*.f64 #s(literal 1/120 binary64) (*.f64 (sin.f64 ky) (*.f64 th th))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (sin.f64 ky) (*.f64 th th)) (*.f64 #s(literal 1/120 binary64) (sin.f64 ky)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (sqrt.f64 #s(literal 2 binary64))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 kx kx) (sin.f64 ky)) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
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(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (neg (* -2 kx))))))
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(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #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)))))))))
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(+ (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))))))))))
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(+ (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)))))))))))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
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(pow ky 2)
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(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
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(pow (sin ky) 2)
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(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
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(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
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(pow (sin ky) 2)
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(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(* -1/6 th)
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(* -1/6 th)
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(* -1/6 th)
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(* -1/6 th)
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(* -1/6 th)
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(* -1/6 th)
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(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
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(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
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(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
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(pow (sin kx) 2)
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(pow (sin kx) 2)
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(pow (sin kx) 2)
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(pow (sin kx) 2)
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(pow (sin kx) 2)
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(pow (sin kx) 2)
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(pow ky 2)
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(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
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(+ 1/2 (* -1/2 (cos (* 2 ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
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(+ 1/2 (* -1/2 (cos (* 2 ky))))
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(+ 1/2 (* -1/2 (cos (* 2 ky))))
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(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
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(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
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(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
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(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
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(sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))
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(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))
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(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
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(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
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(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(fma.f64 (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (*.f64 ky ky) (fma.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) #s(literal 1/4 binary64) #s(literal 1/3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 ky ky) (/.f64 (-.f64 #s(literal 2/45 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) #s(literal 1/4 binary64) #s(literal 1/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) #s(literal 1/4 binary64) #s(literal 1/3 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))

rewrite237.0ms (1.7%)

Memory
-11.6MiB live, 286.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
1 628×lower-fma.f32
1 616×lower-fma.f64
1 292×lower-*.f32
1 268×lower-*.f64
974×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077427
0127421
1441351
03266308
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
30 → 541
Calls
Call 1
Inputs
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (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 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))
(fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)
(*.f64 th (*.f64 th #s(literal -1/6 binary64)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 th)
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(*.f64 th #s(literal -1/6 binary64))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64)))
(+.f64 (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 kx))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx)))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx)))))) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal 1/2 binary64) (neg.f64 (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
(fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
(fma.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64)) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/4 binary64))) (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1/8 binary64)) (-.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64)) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/4 binary64))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))
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(fma.f64 (*.f64 th (*.f64 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 th (*.f64 th #s(literal -1/6 binary64))) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64) #s(literal 1 binary64)) (*.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(/.f64 (*.f64 (sin.f64 ky) (fma.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64) #s(literal -1 binary64))) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) #s(literal 1 binary64)) (sin.f64 ky)) (-.f64 (fma.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64) #s(literal 1 binary64)) (*.f64 th (*.f64 th #s(literal -1/6 binary64)))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64) #s(literal -1 binary64)) (sin.f64 ky)) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal -1 binary64)))
(*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx))))
(+.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) (-.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 kx))))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64))) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.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 kx)))))) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.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 kx))))))) (neg.f64 (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) (neg.f64 (cos.f64 (+.f64 kx kx)))) (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) (neg.f64 (cos.f64 (+.f64 kx kx))))) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.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 kx)))))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64)))
(hypot.f64 (sin.f64 ky) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 ky))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 kx))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)))

eval180.0ms (1.3%)

Memory
28.5MiB live, 369.5MiB allocated
Compiler

Compiled 40 332 to 3 216 computations (92% saved)

prune357.0ms (2.5%)

Memory
-5.0MiB live, 515.5MiB allocated
Pruning

77 alts after pruning (73 fresh and 4 done)

PrunedKeptTotal
New1 225461 271
Fresh142741
Picked325
Done022
Total1 242771 319
Accuracy
100.0%
Counts
1 319 → 77
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.2%
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
11.6%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
77.1%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
18.1%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
77.3%
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky)))
76.4%
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))) #s(literal -1 binary64)))
77.2%
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky))
✓99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
50.0%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
57.8%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
52.2%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
18.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
✓77.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
39.9%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
37.4%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/315 binary64) (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
39.6%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
37.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
39.7%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
43.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
28.1%
(*.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))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
29.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
31.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
33.1%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
32.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
33.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
▶29.0%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
77.2%
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky)) (sin.f64 th))
53.2%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))) (sin.f64 th))
77.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
30.7%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
▶32.9%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
77.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
39.8%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
40.3%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
30.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
▶85.1%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
29.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky ky))))))
31.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
32.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx))))
25.1%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
25.2%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
25.1%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
30.9%
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
24.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
28.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
28.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
30.9%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
27.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
30.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
45.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
✓30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
14.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
14.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) th)))
✓14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
5.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))))))
14.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))))))
14.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th)))))))
14.0%
#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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
5.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
▶11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
28.3%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
39.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
▶28.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
39.8%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
15.5%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky))))))
40.4%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
18.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
24.4%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
25.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
20.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
21.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
15.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
17.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
15.0%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
15.5%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
Compiler

Compiled 3 939 to 2 475 computations (37.2% saved)

simplify227.0ms (1.6%)

Memory
26.8MiB live, 103.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
✓cost-diff0
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
✓cost-diff128
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓cost-diff384
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
✓cost-diff0
(sin.f64 th)
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(*.f64 (sin.f64 ky) (sin.f64 th))
✓cost-diff0
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
✓cost-diff0
(sin.f64 th)
✓cost-diff0
(*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
✓cost-diff0
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
✓cost-diff0
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
✓cost-diff0
#s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))
✓cost-diff0
#s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))
✓cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
✓cost-diff0
(sin.f64 th)
✓cost-diff0
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
✓cost-diff0
(sin.f64 ky)
✓cost-diff0
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
Rules
3 544×lower-fma.f32
3 534×lower-fma.f64
1 624×lower-*.f32
1 596×lower-*.f64
784×lower-+.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
085680
0135661
1224655
2416651
3871635
41442635
51669635
61804635
71988635
82200627
92498627
103194627
113671627
123842627
133882627
143897627
153903627
163903627
03903611
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(sin.f64 ky)
ky
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 th)
th
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))
#s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
#s(literal -1/6 binary64)
(*.f64 th (*.f64 th th))
th
(*.f64 th th)
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64))))
(sin.f64 th)
th
(*.f64 ky (sqrt.f64 #s(literal 2 binary64)))
ky
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(cos.f64 (*.f64 kx #s(literal -2 binary64)))
(*.f64 kx #s(literal -2 binary64))
kx
#s(literal -2 binary64)
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 ky)
ky
(sin.f64 th)
th
(sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
#s(literal 1 binary64)
(cos.f64 (*.f64 kx #s(literal -2 binary64)))
(*.f64 kx #s(literal -2 binary64))
kx
#s(literal -2 binary64)
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
#s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
ky
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 ky ky)
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
(sin.f64 th)
th
Outputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 ky)
ky
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 th)
th
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
#s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th)))))
#s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))
#s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))))
#s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))
#s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th)))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))
#s(literal -1/6 binary64)
(*.f64 th (*.f64 th th))
th
(*.f64 th th)
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64))))
(sin.f64 th)
th
(*.f64 ky (sqrt.f64 #s(literal 2 binary64)))
ky
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(cos.f64 (*.f64 kx #s(literal -2 binary64)))
(*.f64 kx #s(literal -2 binary64))
kx
#s(literal -2 binary64)
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 ky)
ky
(sin.f64 th)
th
(sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
#s(literal 1 binary64)
(cos.f64 (*.f64 kx #s(literal -2 binary64)))
(*.f64 kx #s(literal -2 binary64))
kx
#s(literal -2 binary64)
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) #s(approx (sin ky) (fma.f64 (fma.f64 ky (*.f64 ky (fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))))
(/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 #s(approx (sin ky) (fma.f64 (fma.f64 ky (*.f64 ky (fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))))
#s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
#s(approx (sin ky) (fma.f64 (fma.f64 ky (*.f64 ky (fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(fma.f64 (fma.f64 ky (*.f64 ky (fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)
ky
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(*.f64 ky ky)
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(fma.f64 ky (*.f64 ky (fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))
(fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(fma.f64 ky (*.f64 ky #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
(sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(cos.f64 (+.f64 kx kx))
(+.f64 kx kx)
kx
#s(literal 1/2 binary64)
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
(*.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (+.f64 ky ky))
(+.f64 ky ky)
(sin.f64 th)
th

localize652.0ms (4.6%)

Memory
-17.7MiB live, 652.3MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy94.9%
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
✓accuracy76.7%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
✓accuracy51.3%
#s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
✓accuracy96.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
✓accuracy93.5%
(sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
✓accuracy47.2%
#s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
✓accuracy96.2%
(*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
✓accuracy79.9%
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
✓accuracy74.4%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
✓accuracy39.1%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
✓accuracy99.8%
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
✓accuracy53.0%
#s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))
✓accuracy50.2%
#s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))
✓accuracy30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
✓accuracy99.6%
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
✓accuracy99.6%
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
✓accuracy94.9%
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓accuracy76.7%
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
Samples
255.0ms124×2valid
95.0ms47×1valid
45.0ms70×0valid
31.0ms15×3valid
Compiler

Compiled 530 to 69 computations (87% saved)

Precisions
Click to see histograms. Total time spent on operations: 332.0ms
ival-mult: 73.0ms (22% of total)
ival-cos: 72.0ms (21.7% of total)
adjust: 59.0ms (17.8% of total)
ival-sqrt: 29.0ms (8.7% of total)
ival-add: 25.0ms (7.5% of total)
ival-sin: 24.0ms (7.2% of total)
ival-div: 21.0ms (6.3% of total)
const: 14.0ms (4.2% of total)
ival-pow2: 8.0ms (2.4% of total)
ival-sub: 5.0ms (1.5% of total)
exact: 1.0ms (0.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series116.0ms (0.8%)

Memory
-22.3MiB live, 77.4MiB allocated
Counts
27 → 588
Calls
Call 1
Inputs
#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) #<representation binary64>) () ())
#s(alt #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))) (patch #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))) (patch #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))) #<representation binary64>) () ())
#s(alt (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))) (patch (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))) #<representation binary64>) () ())
#s(alt #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (patch #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (patch (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #<representation binary64>) () ())
#s(alt (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (patch (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (patch (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) #<representation binary64>) () ())
#s(alt (*.f64 (sin.f64 ky) (sin.f64 th)) (patch (*.f64 (sin.f64 ky) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) (patch (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th)) (patch (*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (patch (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #<representation binary64>) () ())
#s(alt (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (patch #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (patch (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) #<representation binary64>) () ())
#s(alt #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (patch #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())
Outputs
#s(alt (/ (* ky (sin th)) (sin kx)) (taylor 0 ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))) (taylor 0 ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx)))) (taylor 0 ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx)))) (taylor 0 ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2)))))) (taylor -inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2)))))) (taylor -inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2)))))) (taylor -inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2)))))) (taylor -inf ky) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))))) (taylor 0 th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (taylor -inf th) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))))) (taylor 0 kx) (#s(alt (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (patch (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
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#s(alt (- 1 (cos (* 2 kx))) (taylor inf kx) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())) ())
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#s(alt (- 1 (cos (neg (* -2 kx)))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 kx)))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 kx)))) (taylor -inf kx) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (taylor 0 kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))) (taylor 0 kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))) (taylor 0 kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))) (taylor 0 kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))) (taylor -inf kx) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))) (taylor 0 ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) #<representation binary64>) () ())) ())
Calls

147 calls:

TimeVariablePointExpression
63.0ms
kx
@-inf
(/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))
1.0ms
th
@inf
(* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2))))))
1.0ms
ky
@0
(* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2))))))
1.0ms
kx
@inf
(* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2))))))
1.0ms
kx
@0
(* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2))))))

simplify807.0ms (5.7%)

Memory
-96.2MiB live, 701.8MiB allocated
Algorithm
1×egg-herbie
Rules
7 760×lower-fma.f64
7 760×lower-fma.f32
7 286×lower-*.f64
7 286×lower-*.f32
5 876×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
090616053
1297715255
2703215165
0868814231
Stop Event
1×iter limit
1×node limit
Counts
588 → 583
Calls
Call 1
Inputs
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* th (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(/ (sin th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
(sin th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (pow th 3))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* -1/6 (pow th 3))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* ky (* th (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* th (+ (* -1/6 (* (* ky (* (pow th 2) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))))
(* th (+ (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow th 2) (+ (* -1/6 (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* 1/120 (* (* ky (* (pow th 2) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))))))))
(* th (+ (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow th 2) (+ (* -1/6 (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/5040 (* (* ky (* (pow th 2) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* 1/120 (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))))))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(/ (* ky (* (sin th) (* (sqrt 1/2) (sqrt 2)))) kx)
(/ (+ (* 1/12 (/ (* (pow kx 2) (* ky (* (sin th) (sqrt 2)))) (sqrt 1/2))) (* ky (* (sin th) (* (sqrt 1/2) (sqrt 2))))) kx)
(/ (+ (* ky (* (sin th) (* (sqrt 1/2) (sqrt 2)))) (* (pow kx 2) (+ (* 1/12 (/ (* ky (* (sin th) (sqrt 2))) (sqrt 1/2))) (* 1/2 (/ (* (pow kx 2) (* ky (* (sin th) (* (sqrt 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))))))) (sqrt 1/2)))))) kx)
(/ (+ (* ky (* (sin th) (* (sqrt 1/2) (sqrt 2)))) (* (pow kx 2) (+ (* 1/12 (/ (* ky (* (sin th) (sqrt 2))) (sqrt 1/2))) (* (pow kx 2) (+ (* 1/2 (/ (* ky (* (sin th) (* (sqrt 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))) (sqrt 1/2))) (* 1/2 (/ (* (pow kx 2) (* ky (* (sin th) (* (sqrt 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))))))) (sqrt 1/2)))))))) kx)
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
(* ky (* th (sqrt 2)))
(* th (+ (* -1/6 (* ky (* (pow th 2) (sqrt 2)))) (* ky (sqrt 2))))
(* th (+ (* ky (sqrt 2)) (* (pow th 2) (+ (* -1/6 (* ky (sqrt 2))) (* 1/120 (* ky (* (pow th 2) (sqrt 2))))))))
(* th (+ (* ky (sqrt 2)) (* (pow th 2) (+ (* -1/6 (* ky (sqrt 2))) (* (pow th 2) (+ (* -1/5040 (* ky (* (pow th 2) (sqrt 2)))) (* 1/120 (* ky (sqrt 2)))))))))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* ky (* (sin th) (sqrt 2)))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 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))))))))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* 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) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow kx 2)))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
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(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
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(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))
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(+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 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))))
(+ 1/2 (* -1/2 (cos (* 2 ky))))
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(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* -1/2 (cos (neg (* -2 ky)))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
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(+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(pow ky 2)
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(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))
(sin kx)
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(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
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(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(/ (sqrt 1/2) kx)
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx)
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx)
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx)
(sqrt (/ 1 (- 1 (cos (* -2 kx)))))
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(sqrt (/ 1 (- 1 (cos (* -2 kx)))))
(sqrt (/ 1 (- 1 (cos (* -2 kx)))))
(sqrt (/ 1 (- 1 (cos (* -2 kx)))))
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(- 1 (cos (* -2 kx)))
(/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))
(+ (* -1 (/ (pow kx 2) (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2)))) (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2)))) (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(/ 2 (- 1 (cos (* 2 kx))))
(+ (* -4 (/ (pow ky 2) (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* -1/2 (* (pow kx 2) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (* 1/2 (* (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* -2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (pow ky 2) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 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 ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
Outputs
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/5040 binary64)) (*.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))))))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 th (sin.f64 ky)))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 #s(literal -1/6 binary64) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (sin.f64 ky) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 4 binary64)))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 ky (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(* th (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 th (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))
(*.f64 th (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(* th (+ (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))) (* 1/120 (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64))) (*.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
(*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
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(+ (* -1/2 (* (* (pow kx 2) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (*.f64 (sin.f64 th) (*.f64 kx kx))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
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(+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(/ (sin th) (sin kx))
(/.f64 (sin.f64 th) (sin.f64 kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 ky ky) (/.f64 (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 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 ky ky)) (*.f64 (*.f64 (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 (*.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))) (* (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 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (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 (*.f64 #s(literal -1/2 binary64) (*.f64 ky ky)) (*.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))))) (/.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)))
(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
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(* (sin th) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (pow (sin kx) 2))))))
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th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
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(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))))))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/5040 binary64)) (*.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))))))) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 th) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))) (/.f64 (*.f64 #s(literal -1/2 binary64) (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))) (* (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 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (*.f64 (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (sin.f64 th)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (*.f64 th (*.f64 th th)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th))))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (*.f64 th (*.f64 th th)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th))))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (*.f64 th (*.f64 th th)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th))))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 th th))) (neg.f64 (*.f64 th (*.f64 th th))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 th th))) (neg.f64 (*.f64 th (*.f64 th th))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 th th))) (neg.f64 (*.f64 th (*.f64 th th))))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* -1/6 (pow th 3))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(*.f64 (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (/.f64 (*.f64 #s(literal -2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (/.f64 (*.f64 #s(literal -2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 th) (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/12 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (/.f64 (*.f64 #s(literal -1/60 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (/.f64 (*.f64 #s(literal -2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* ky (* th (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* th (+ (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))) (* (pow th 2) (+ (* -1/6 (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))) (* 1/120 (* (* ky (* (pow th 2) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx)))))))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(/ (+ (* ky (* (sin th) (* (sqrt 1/2) (sqrt 2)))) (* (pow kx 2) (+ (* 1/12 (/ (* ky (* (sin th) (sqrt 2))) (sqrt 1/2))) (* 1/2 (/ (* (pow kx 2) (* ky (* (sin th) (* (sqrt 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))))))) (sqrt 1/2)))))) kx)
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(/ (+ (* ky (* (sin th) (* (sqrt 1/2) (sqrt 2)))) (* (pow kx 2) (+ (* 1/12 (/ (* ky (* (sin th) (sqrt 2))) (sqrt 1/2))) (* (pow kx 2) (+ (* 1/2 (/ (* ky (* (sin th) (* (sqrt 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))) (sqrt 1/2))) (* 1/2 (/ (* (pow kx 2) (* ky (* (sin th) (* (sqrt 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))))))) (sqrt 1/2)))))))) kx)
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* -2 kx))))))
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(* ky (* th (sqrt 2)))
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(* th (+ (* -1/6 (* ky (* (pow th 2) (sqrt 2)))) (* ky (sqrt 2))))
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(* th (+ (* ky (sqrt 2)) (* (pow th 2) (+ (* -1/6 (* ky (sqrt 2))) (* 1/120 (* ky (* (pow th 2) (sqrt 2))))))))
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(* th (+ (* ky (sqrt 2)) (* (pow th 2) (+ (* -1/6 (* ky (sqrt 2))) (* (pow th 2) (+ (* -1/5040 (* ky (* (pow th 2) (sqrt 2)))) (* 1/120 (* ky (sqrt 2)))))))))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* ky (* (sin th) (sqrt 2)))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (sin.f64 ky) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 4 binary64)))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* ky (sin th))
(*.f64 ky (sin.f64 th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(*.f64 ky (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (sin.f64 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))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 (sin.f64 th) #s(literal -1/6 binary64))) (sin.f64 th)))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* (sin ky) (sin th))
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(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (sin.f64 ky) (*.f64 (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal -3/8 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 2/45 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 2/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 4 binary64)))))))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (+.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64))))))))) (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))))
(*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))))))))))
(*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (sqrt.f64 #s(literal 2 binary64))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/3 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 #s(literal 1/120 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (fma.f64 (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 1/120 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (fma.f64 (*.f64 ky ky) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal -1/5040 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (/.f64 #s(literal -1/60 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))))) (fma.f64 (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (*.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
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(sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))
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(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* -1/2 (* (pow kx 2) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (* 1/2 (* (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
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(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 ky)))) 3)))))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx)))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
(* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(+ (* -2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(fma.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 ky ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (pow ky 2) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (/.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (*.f64 (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))))
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 16 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (+.f64 (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64)))))) (/.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(literal 3 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 ky (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(* 2 (pow kx 2))
(*.f64 #s(literal 2 binary64) (*.f64 kx kx))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64)))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64)))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
(sqrt (+ 1/2 (* -1/2 (cos (* 2 ky)))))
(sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))))))
(fma.f64 (*.f64 kx kx) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 kx kx) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky))))))) (+ 1/2 (* -1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 ky)))))))))))))
(fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 kx kx) (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (neg (* -2 kx))))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (/.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(fma.f64 (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (*.f64 ky ky) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 ky))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (neg (* -2 ky)))) (* 1/2 (- 1 (cos (* 2 kx)))))))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))

rewrite173.0ms (1.2%)

Memory
11.3MiB live, 322.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
1 526×lower-*.f32
1 498×lower-*.f64
1 452×lower-fma.f32
1 442×lower-fma.f64
1 070×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
085484
0135467
1456451
02989440
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
27 → 263
Calls
Call 1
Inputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(sin.f64 ky)
(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sin.f64 th)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))
#s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))
(*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
(*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))
#s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
(sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))
Outputs
(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))) (sin.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) (*.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) (neg.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))) (sin.f64 th)))
(/.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 th))) (neg.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))))))
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#s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))
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(*.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)))

eval185.0ms (1.3%)

Memory
-11.5MiB live, 270.5MiB allocated
Compiler

Compiled 30 818 to 1 994 computations (93.5% saved)

prune253.0ms (1.8%)

Memory
13.1MiB live, 524.5MiB allocated
Pruning

91 alts after pruning (86 fresh and 5 done)

PrunedKeptTotal
New90032932
Fresh145468
Picked415
Done044
Total918911 009
Accuracy
100.0%
Counts
1 009 → 91
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.2%
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
11.6%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
77.1%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
18.1%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
76.4%
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))) #s(literal -1 binary64)))
77.2%
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky))
✓99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
50.0%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
57.8%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
52.2%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
18.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
✓77.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
39.9%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
43.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
28.1%
(*.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))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
29.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
31.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
33.1%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
32.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
33.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
29.0%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
37.4%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
37.5%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
37.2%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
37.4%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
77.2%
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky)) (sin.f64 th))
53.2%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))) (sin.f64 th))
33.1%
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
77.1%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
30.7%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
18.7%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
19.0%
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
28.0%
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
77.1%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
39.8%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
40.3%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
30.7%
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
47.3%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky ky))))))
29.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky ky))))))
31.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
32.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx))))
25.1%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
25.2%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
25.1%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
30.9%
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
28.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
28.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
30.9%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
18.2%
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
28.3%
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
27.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
30.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
✓30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
14.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
14.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) th)))
✓14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
5.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))))))
14.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))))))
14.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th)))))))
14.0%
#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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
5.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
✓11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
28.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
28.4%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
39.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
28.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
28.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
28.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
16.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
17.8%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
16.6%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
17.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
14.7%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
20.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
15.5%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
15.5%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
39.8%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
40.4%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
18.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
24.4%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
25.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
20.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
21.3%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
15.2%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
17.9%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
15.6%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
21.5%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
15.0%
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
Compiler

Compiled 5 562 to 2 006 computations (63.9% saved)

regimes429.0ms (3%)

Memory
15.2MiB live, 839.7MiB allocated
Counts
138 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
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(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 ky (fma.f64 ky (/.f64 (*.f64 ky (*.f64 #s(literal -1/2 binary64) (sin.f64 th))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))))))
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky 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 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal -1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))) #s(literal 1/4 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))) #s(literal -1 binary64)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Calls

9 calls:

68.0ms
ky
50.0ms
kx
47.0ms
(sin.f64 ky)
47.0ms
(sin.f64 th)
46.0ms
(*.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
AccuracySegmentsBranch
99.7%1kx
99.7%1ky
99.7%1th
99.7%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.7%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.7%1(sin.f64 ky)
99.7%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.7%1(sin.f64 kx)
99.7%1(sin.f64 th)
Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes362.0ms (2.5%)

Memory
-16.8MiB live, 676.8MiB allocated
Counts
127 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
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#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 (*.f64 kx kx) (fma.f64 kx (*.f64 kx #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky)))
Calls

9 calls:

47.0ms
(sin.f64 th)
44.0ms
th
43.0ms
kx
39.0ms
(*.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))
38.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
99.4%2kx
99.3%2ky
87.3%2th
88.8%5(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.5%4(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.3%3(sin.f64 ky)
99.4%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.5%3(sin.f64 kx)
87.4%3(sin.f64 th)
Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes111.0ms (0.8%)

Memory
6.8MiB live, 117.5MiB allocated
Counts
120 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
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#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/315 binary64) (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 ky)) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
Calls

2 calls:

70.0ms
kx
33.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
99.4%2kx
99.4%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes333.0ms (2.3%)

Memory
-6.8MiB live, 471.7MiB allocated
Counts
114 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
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(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
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(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/315 binary64) (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 ky (*.f64 ky (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (sin.f64 kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))
Calls

8 calls:

59.0ms
(sin.f64 kx)
54.0ms
(sin.f64 ky)
41.0ms
th
36.0ms
kx
34.0ms
ky
Results
AccuracySegmentsBranch
76.8%3(sin.f64 th)
76.4%2th
89.0%5(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
79.3%3(sin.f64 ky)
80.7%3(sin.f64 kx)
81.5%3ky
80.9%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
79.4%2kx
Compiler

Compiled 50 to 38 computations (24% saved)

regimes70.0ms (0.5%)

Memory
2.9MiB live, 121.0MiB allocated
Counts
104 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/315 binary64) (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
Calls

2 calls:

31.0ms
(/.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)))))
31.0ms
(*.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
AccuracySegmentsBranch
67.6%6(*.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))
88.9%6(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 35 to 24 computations (31.4% saved)

regimes277.0ms (1.9%)

Memory
22.7MiB live, 418.6MiB allocated
Counts
103 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
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(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/315 binary64) (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (*.f64 ky (*.f64 ky ky)) ky)) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

8 calls:

48.0ms
(sin.f64 ky)
35.0ms
(sin.f64 th)
33.0ms
(sin.f64 kx)
33.0ms
ky
32.0ms
th
Results
AccuracySegmentsBranch
60.1%3(sin.f64 th)
60.2%2th
71.5%4(sin.f64 ky)
70.5%4(sin.f64 kx)
69.7%4(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
69.0%3kx
73.9%4ky
79.5%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 50 to 38 computations (24% saved)

regimes79.0ms (0.6%)

Memory
-13.6MiB live, 61.6MiB allocated
Counts
98 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
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(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/315 binary64) (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.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 #s(literal -2 binary64))))))) (+.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 ky (*.f64 ky (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

40.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
79.5%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 16 to 11 computations (31.3% saved)

regimes37.0ms (0.3%)

Memory
-5.2MiB live, 75.3MiB allocated
Counts
93 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))))))
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(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 th (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 #s(literal 2/45 binary64) (*.f64 ky ky) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal -1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

27.0ms
(/.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
AccuracySegmentsBranch
79.4%5(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes31.0ms (0.2%)

Memory
28.6MiB live, 66.5MiB allocated
Counts
87 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
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(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
(*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (/.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 #s(literal -1/3 binary64) (*.f64 ky ky) #s(literal 1 binary64))))))) (sin.f64 th))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

25.0ms
(/.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
AccuracySegmentsBranch
79.3%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 16 to 11 computations (31.3% saved)

regimes33.0ms (0.2%)

Memory
-10.4MiB live, 63.0MiB allocated
Counts
83 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
Outputs
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

27.0ms
(/.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
AccuracySegmentsBranch
79.3%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 16 to 11 computations (31.3% saved)

regimes57.0ms (0.4%)

Memory
7.1MiB live, 129.4MiB allocated
Counts
82 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
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(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 kx #s(literal -2 binary64))) #s(literal -1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) (*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2)))) (*.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) (fma.f64 kx kx #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
Outputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
Calls

2 calls:

26.0ms
ky
25.0ms
(/.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
AccuracySegmentsBranch
71.6%3ky
69.8%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 20 to 14 computations (30% saved)

regimes25.0ms (0.2%)

Memory
15.4MiB live, 52.9MiB allocated
Counts
64 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))))
Outputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))
Calls

1 calls:

20.0ms
ky
Results
AccuracySegmentsBranch
71.6%3ky
Compiler

Compiled 4 to 3 computations (25% saved)

regimes159.0ms (1.1%)

Memory
-35.7MiB live, 257.4MiB 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) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (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 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
Outputs
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

7 calls:

36.0ms
(sin.f64 kx)
22.0ms
ky
20.0ms
(*.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))
20.0ms
kx
20.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
51.8%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))
56.4%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
58.6%3(sin.f64 kx)
56.8%3kx
62.2%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
64.1%4(sin.f64 ky)
58.0%3ky
Compiler

Compiled 60 to 44 computations (26.7% saved)

regimes23.0ms (0.2%)

Memory
12.8MiB live, 49.7MiB allocated
Counts
57 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th))
Outputs
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

18.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
64.1%4(sin.f64 ky)
Compiler

Compiled 5 to 4 computations (20% saved)

regimes26.0ms (0.2%)

Memory
13.1MiB live, 51.0MiB allocated
Counts
54 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
Outputs
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.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

1 calls:

22.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
64.0%4(sin.f64 ky)
Compiler

Compiled 5 to 4 computations (20% saved)

regimes59.0ms (0.4%)

Memory
-18.6MiB live, 56.2MiB allocated
Counts
51 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 kx kx #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) #s(approx (+ (* -1/2 (cos (* ky -2))) 1/2) (*.f64 ky ky))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -1/3 binary64) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 th (fma.f64 (*.f64 th th) (fma.f64 (*.f64 th th) (fma.f64 #s(literal -1/5040 binary64) (*.f64 th th) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
Outputs
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

2 calls:

33.0ms
(sin.f64 ky)
22.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
61.7%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
57.8%5(sin.f64 ky)
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes72.0ms (0.5%)

Memory
12.5MiB live, 132.4MiB allocated
Counts
42 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
Outputs
(*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

5 calls:

17.0ms
(sin.f64 th)
14.0ms
ky
13.0ms
th
13.0ms
(sin.f64 kx)
12.0ms
(/.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
AccuracySegmentsBranch
51.4%4ky
55.9%3(sin.f64 kx)
37.9%3(sin.f64 th)
37.1%3th
55.4%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 34 to 25 computations (26.5% saved)

regimes28.0ms (0.2%)

Memory
-13.6MiB live, 64.4MiB allocated
Counts
41 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 ky (sin.f64 th))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))) (*.f64 (fma.f64 th (*.f64 th #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 ky)))))
Outputs
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

2 calls:

13.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
12.0ms
kx
Results
AccuracySegmentsBranch
56.3%3kx
55.1%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 20 to 14 computations (30% saved)

regimes13.0ms (0.1%)

Memory
29.6MiB live, 29.6MiB allocated
Counts
35 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (+ (* (cos (+ ky ky)) -1/2) 1/2) (*.f64 ky 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 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
Outputs
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

10.0ms
(/.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
AccuracySegmentsBranch
55.1%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes14.0ms (0.1%)

Memory
-13.9MiB live, 27.1MiB allocated
Counts
31 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 ky (sin.f64 th))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
(*.f64 #s(approx (* (sin ky) (sin th)) (*.f64 th (sin.f64 ky))) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

12.0ms
(/.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
AccuracySegmentsBranch
55.0%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes38.0ms (0.3%)

Memory
5.3MiB live, 83.4MiB allocated
Counts
28 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
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

4 calls:

9.0ms
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)))))
9.0ms
(sin.f64 kx)
8.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
48.7%3(sin.f64 kx)
45.9%2kx
45.9%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
53.3%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 32 to 24 computations (25% saved)

regimes20.0ms (0.1%)

Memory
-6.2MiB live, 32.0MiB allocated
Counts
27 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

2 calls:

9.0ms
(sin.f64 ky)
8.0ms
(/.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
AccuracySegmentsBranch
45.2%2(sin.f64 ky)
53.0%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes67.0ms (0.5%)

Memory
-9.5MiB live, 87.5MiB allocated
Counts
26 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 #s(approx (* (sin th) (* ky (sqrt 2))) (*.f64 ky (*.f64 th (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 #s(literal 2 binary64) (*.f64 kx kx)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/3 binary64) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (*.f64 ky (*.f64 (*.f64 th (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 #s(approx (sin th) (fma.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th)) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (/ 1 (- 1 (cos (* kx -2))))) (/.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (*.f64 kx kx) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) kx))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (fma.f64 ky (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (sqrt.f64 #s(literal 2 binary64)))))))))
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (*.f64 (sin.f64 th) (*.f64 ky (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- 1 (cos (* kx -2))) (*.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) (fma.f64 (*.f64 kx kx) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))))))
Outputs
#s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

6 calls:

19.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
8.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
8.0ms
(sin.f64 kx)
8.0ms
kx
8.0ms
ky
Results
AccuracySegmentsBranch
43.3%3kx
43.3%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
43.3%4(sin.f64 kx)
42.2%2ky
42.5%3(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
45.5%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 55 to 40 computations (27.3% saved)

regimes60.0ms (0.4%)

Memory
-0.4MiB live, 73.5MiB allocated
Counts
15 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 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)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (fma.f64 (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 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 th (*.f64 th #s(literal -1/6 binary64))) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64))) (*.f64 th (*.f64 th th)) (*.f64 th (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 th (-.f64 th (*.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th))) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th)))))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

7 calls:

25.0ms
(sin.f64 ky)
7.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
5.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
5.0ms
kx
5.0ms
(sin.f64 kx)
Results
AccuracySegmentsBranch
32.7%2(sin.f64 kx)
37.9%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))
33.8%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
33.8%2kx
34.4%2ky
34.8%2(sin.f64 ky)
38.0%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 60 to 44 computations (26.7% saved)

regimes45.0ms (0.3%)

Memory
10.1MiB live, 86.0MiB allocated
Counts
11 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64)) (*.f64 th (*.f64 th th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (-.f64 (*.f64 th th) (*.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th))) (-.f64 th (*.f64 (*.f64 th #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) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 th #s(literal -1/6 binary64)) (*.f64 th th) (neg.f64 th)) (fma.f64 (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) #s(literal 1/36 binary64)) (*.f64 th th) (neg.f64 (*.f64 th th)))))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) th)))
Calls

9 calls:

10.0ms
(sin.f64 th)
6.0ms
kx
4.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
4.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
4.0ms
th
Results
AccuracySegmentsBranch
19.6%3(sin.f64 kx)
19.6%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
19.6%2kx
19.1%2ky
19.3%2(sin.f64 ky)
14.6%1th
14.6%1(sin.f64 th)
22.3%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))
21.8%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 69 to 51 computations (26.1% saved)

regimes6.0ms (0%)

Memory
15.2MiB live, 15.2MiB allocated
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.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) (fma.f64 (*.f64 th th) (*.f64 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) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th)))
Calls

2 calls:

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
(/.f64 (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
AccuracySegmentsBranch
21.8%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)))))
21.8%2(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 35 to 24 computations (31.4% saved)

regimes22.0ms (0.2%)

Memory
-28.6MiB live, 44.1MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

9 calls:

4.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
4.0ms
th
2.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
2.0ms
(sin.f64 kx)
2.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
11.4%1th
11.4%1(sin.f64 th)
11.4%1(sin.f64 kx)
11.4%1ky
11.4%1(sin.f64 ky)
11.4%1kx
11.4%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
11.4%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
11.4%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 69 to 51 computations (26.1% saved)

bsearch1.0ms (0%)

Memory
2.4MiB live, 2.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
7.971292274196741e-17
2.0768960991741258e-7
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch31.0ms (0.2%)

Memory
12.8MiB live, 53.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
29.0ms
8.928209380495476e-9
0.00045572977113168594
Samples
23.0ms128×0valid
Compiler

Compiled 414 to 282 computations (31.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-sin: 14.0ms (70.1% of total)
ival-pow2: 2.0ms (10% of total)
ival-div: 1.0ms (5% of total)
ival-add: 1.0ms (5% of total)
ival-mult: 1.0ms (5% of total)
ival-sqrt: 1.0ms (5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
2.9MiB live, 2.9MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.990669322958426
0.9999975523967313
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
2.8MiB live, 2.8MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.000000000000025
0.0ms
0.9999975523967313
0.9999999999999831
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
2.4MiB live, 2.4MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999975523967313
0.9999999999999831
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999975523967313
0.9999999999999831
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999975523967313
0.9999999999999831
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999975523967313
0.9999999999999831
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999975523967313
0.9999999999999831
0.0ms
0.31682460121683265
0.36756519675434624
0.0ms
-0.19717281774104473
-0.16218895214593443
0.0ms
-1.0
-0.9999299660324412
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch55.0ms (0.4%)

Memory
10.3MiB live, 118.7MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
23.0ms
0.23422517832592937
98.29034239776603
29.0ms
2.582673684366985e-160
2.024833434025682e-157
Samples
41.0ms256×0valid
Compiler

Compiled 1 190 to 674 computations (43.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-sin: 18.0ms (53.1% of total)
ival-div: 7.0ms (20.6% of total)
ival-pow2: 5.0ms (14.7% of total)
ival-mult: 2.0ms (5.9% of total)
ival-sqrt: 2.0ms (5.9% of total)
ival-add: 1.0ms (2.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch3.0ms (0%)

Memory
6.6MiB live, 6.6MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
1.0ms
0.23422517832592937
98.29034239776603
1.0ms
2.582673684366985e-160
2.024833434025682e-157
Compiler

Compiled 1 190 to 674 computations (43.4% saved)

bsearch1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.0026745300915458027
0.002925700511741941
0.0ms
2.582673684366985e-160
2.024833434025682e-157
0.0ms
-0.01388823298608454
3.273368950237134e-298
Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch7.0ms (0.1%)

Memory
-41.8MiB live, 1.4MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.0026745300915458027
0.002925700511741941
0.0ms
2.582673684366985e-160
2.024833434025682e-157
7.0ms
-0.01388823298608454
3.273368950237134e-298
Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.0026745300915458027
0.002925700511741941
0.0ms
2.582673684366985e-160
2.024833434025682e-157
0.0ms
-0.01388823298608454
3.273368950237134e-298
Compiler

Compiled 21 to 18 computations (14.3% saved)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.0031813777284576197
0.025736093034777047
0.0ms
-0.16218895214593443
3.7241852058020714e-298
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0031813777284576197
0.025736093034777047
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0031813777284576197
0.025736093034777047
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0031813777284576197
0.025736093034777047
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.0031813777284576197
0.025736093034777047
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.5563217449033084e-6
0.0031813777284576197
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.5563217449033084e-6
0.0031813777284576197
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
6.054308936020809e-13
5.4858041181725905e-9
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch14.0ms (0.1%)

Memory
26.3MiB live, 26.3MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
5.470125482236468e-46
4.173505757042695e-40
Samples
8.0ms144×0valid
Compiler

Compiled 211 to 136 computations (35.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sin: 3.0ms (67.8% of total)
ival-mult: 1.0ms (22.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.637988007817466e-309
2.3250205188905514e-306
Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch10.0ms (0.1%)

Memory
-21.1MiB live, 18.2MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
10.0ms
5.470125482236468e-46
4.173505757042695e-40
Samples
6.0ms96×0valid
Compiler

Compiled 274 to 163 computations (40.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sin: 2.0ms (52.7% of total)
ival-mult: 1.0ms (26.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify38.0ms (0.3%)

Memory
-9.0MiB live, 68.9MiB allocated
Algorithm
1×egg-herbie
Rules
102×*-commutative_binary64
14×+-commutative_binary64
8×sub-neg_binary64
4×neg-sub0_binary64
4×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03393499
13983499
24043499
34083499
44103499
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky))))
(if (<=.f64 kx #s(literal 4150517416584649/9223372036854775808 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.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 -1 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3242591731706757/18014398509481984 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) #s(approx (/ (sin th) (/ 1 (sin ky))) (*.f64 th (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 3152519739159347/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 th (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 ky #s(literal -2 binary64))) #s(literal 1/2 binary64))))) #s(approx (* (+ (* th (* th -1/6)) 1) (sin ky)) (sin.f64 ky))))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th))))))
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(if (<=.f64 ky #s(literal 2127041452668699/494660802946209068121005042039294380070262698202423679828126112185794450213063734340632802122486089979195342852032278678702730068613502419935092310203786335833213544297398272 binary64)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx)))) (if (<=.f64 ky #s(literal 2206763817411543/4503599627370496 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))))))) (sin.f64 th)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))))))
(if (<=.f64 (sin.f64 ky) #s(literal -5764607523034235/576460752303423488 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))) (if (<=.f64 (sin.f64 ky) #s(literal 7914572847139345/15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704 binary64)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (+ (* (cos (+ ky ky)) -1/2) 1/2))) (sin.f64 kx)))) (if (<=.f64 (sin.f64 ky) #s(literal 6456360425798343/2305843009213693952 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))
(if (<=.f64 (sin.f64 ky) #s(literal -5764607523034235/576460752303423488 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))) (if (<=.f64 (sin.f64 ky) #s(literal 7914572847139345/15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) (if (<=.f64 (sin.f64 ky) #s(literal 6456360425798343/2305843009213693952 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))
(if (<=.f64 (sin.f64 ky) #s(literal -5764607523034235/576460752303423488 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)))))) (if (<=.f64 (sin.f64 ky) #s(literal 7914572847139345/15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) (if (<=.f64 (sin.f64 ky) #s(literal 6456360425798343/2305843009213693952 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 ky (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) #s(approx (+ 1/2 (* -1/2 (cos (+ ky ky)))) (*.f64 ky ky))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* th (* (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* kx -2)))) (+ (* -1/2 (cos (* ky -2))) 1/2)))) (* (+ (* th (* th -1/6)) 1) (sin ky)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (*.f64 th (sin.f64 ky)) (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #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 5764607523034235/1152921504606846976 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 binary64)) (*.f64 (*.f64 #s(approx (sin ky) (fma.f64 ky (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) ky)) (sin.f64 th)) (sqrt.f64 #s(approx (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) (*.f64 (/.f64 (*.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))) (sin.f64 th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (*.f64 ky (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* 1/2 (cos (+ kx kx)))) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal -2 binary64)))))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5902958103587057/1180591620717411303424 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5902958103587057/1180591620717411303424 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/4951760157141521099596496896 binary64)) #s(approx (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ kx kx))) 1/2) (+ 1/2 (* -1/2 (cos (+ ky ky)))))))) #s(approx (* (* (sin th) (* ky (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* kx -2)))))) (*.f64 ky (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (sin.f64 th) kx))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4499426523925173/1606938044258990275541962092341162602522202993782792835301376 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 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 1012011266536553/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) 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 728143801304855/50216813883093446110686315385661331328818843555712276103168 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky))))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx))))) (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (sin.f64 ky))))
(if (<=.f64 kx #s(literal 4150517416584649/9223372036854775808 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx)))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))) (sin.f64 th)))
(if (<=.f64 kx #s(literal 4150517416584649/9223372036854775808 binary64)) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (fma.f64 kx (*.f64 #s(literal -1/6 binary64) (*.f64 kx kx)) kx))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))))
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(if (<=.f64 (*.f64 (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)))))) #s(literal 1012011266536553/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 (*.f64 th th) (fma.f64 #s(literal 1/120 binary64) (*.f64 th th) #s(literal -1/6 binary64))) 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 728143801304855/50216813883093446110686315385661331328818843555712276103168 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th)))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 th (*.f64 th (*.f64 th #s(literal -1/6 binary64))) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* th (* th (* th -1/6))) th) (*.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 th th))))))

soundness2.0s (14%)

Memory
53.5MiB live, 1 745.2MiB allocated
Rules
14 278×lower-fma.f64
14 278×lower-fma.f32
12 454×lower-fma.f64
12 454×lower-fma.f32
9 136×lower-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045238
077227
1277200
01983200
085484
0135467
1456451
02989440
090616053
1297715255
2703215165
0868814231
03172263
110112214
238602122
378042122
081071974
0111517975
1379117082
0825815995
066811658
1217111177
2792411151
0812110384
01349
02249
16249
233849
3290249
0828434
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 4 224 to 1 579 computations (62.6% saved)

preprocess206.0ms (1.4%)

Memory
-9.8MiB live, 420.5MiB allocated
Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 4 428 to 566 computations (87.2% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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