Toniolo and Linder, Equation (3b), real

Time bar (total: 12.9s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze432.0ms (3.3%)

Memory
-84.6MiB live, 388.6MiB 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)

sample1.8s (13.9%)

Memory
69.3MiB live, 2 277.0MiB allocated
Samples
1.4s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.1s
ival-sin: 643.0ms (59% of total)
ival-pow2: 208.0ms (19.1% of total)
ival-div: 65.0ms (6% of total)
ival-sqrt: 61.0ms (5.6% of total)
ival-mult: 55.0ms (5% of total)
ival-add: 47.0ms (4.3% of total)
ival-true: 7.0ms (0.6% of total)
ival-assert: 4.0ms (0.4% of total)
Bogosity

explain317.0ms (2.5%)

Memory
-6.6MiB live, 231.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
160-1(4.917224460967247e-158 -1.5810935753930972e-194 7.600522070498472e-266)(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-rescue150
↳(pow.f64 (sin.f64 kx) #s(literal 2 binary64))underflow63
↳(pow.f64 (sin.f64 ky) #s(literal 2 binary64))underflow71
↳(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))underflow15
Confusion
Predicted +Predicted -
+151
-0240
Precision
1.0
Recall
0.9375
Confusion?
Predicted +Predicted MaybePredicted -
+1501
-00240
Precision?
1.0
Recall?
0.9375
Freqs
test
numberfreq
0241
115
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
175.0ms512×0valid
Compiler

Compiled 152 to 43 computations (71.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 110.0ms
ival-sqrt: 57.0ms (51.7% of total)
ival-sin: 33.0ms (30% of total)
ival-pow2: 10.0ms (9.1% of total)
ival-div: 3.0ms (2.7% 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)

preprocess255.0ms (2%)

Memory
11.3MiB live, 150.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045153
189147
2211147
3416147
4898147
52624147
65843147
01316
02216
13016
24816
310316
420516
544616
6115816
7293016
8699416
0807211
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶93.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify170.0ms (1.3%)

Memory
-21.9MiB live, 113.9MiB 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-diff5
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01366
02266
13066
24866
310366
420566
544666
6115866
7293066
8699466
0807251
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th

localize82.0ms (0.6%)

Memory
6.1MiB live, 60.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.171875
(*.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))
accuracy0.2109375
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy0.28353500976844204
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy3.778950357878138
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
Samples
73.0ms256×0valid
Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 63.0ms
ival-sin: 37.0ms (58.6% of total)
ival-pow2: 20.0ms (31.7% of total)
ival-div: 2.0ms (3.2% of total)
ival-mult: 2.0ms (3.2% of total)
ival-sqrt: 2.0ms (3.2% of total)
ival-add: 1.0ms (1.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series51.0ms (0.4%)

Memory
-4.2MiB live, 41.0MiB allocated
Counts
6 → 45
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Outputs
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(pow (sin kx) 2)
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(pow (sin ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
Calls

9 calls:

TimeVariablePointExpression
27.0ms
ky
@0
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
4.0ms
th
@-inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms
kx
@inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms
kx
@0
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms
kx
@-inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))

simplify197.0ms (1.5%)

Memory
19.6MiB live, 198.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03171402
111341336
252361308
084061228
Stop Event
1×iter limit
1×node limit
Counts
45 → 44
Calls
Call 1
Inputs
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(pow (sin kx) 2)
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(pow (sin ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
Outputs
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (/.f64 (fma.f64 (*.f64 kx kx) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) #s(literal 1/2 binary64)) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 kx kx) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 ky)) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 kx kx)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)))) (*.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (*.f64 (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) kx (fma.f64 (pow.f64 kx #s(literal 4 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (*.f64 kx kx) (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (*.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 th)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (*.f64 (*.f64 kx kx) #s(literal 1/2 binary64)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) (*.f64 (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) kx) kx) #s(literal 1/3 binary64)) (*.f64 kx kx))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (/.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) #s(literal 1/2 binary64)) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 ky ky) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 th) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx)) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (sin.f64 th)) (/.f64 (*.f64 #s(literal 1/120 binary64) (sin.f64 th)) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 th) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx))) (*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 (fma.f64 (*.f64 (*.f64 (sin.f64 kx) #s(literal -1/2 binary64)) (sin.f64 th)) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (fma.f64 (*.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (sin.f64 th)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 (fma.f64 #s(literal -1/5040 binary64) (sin.f64 th) (/.f64 (*.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (sin.f64 th)) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (*.f64 ky ky) (/.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 th) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx))) (*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/6 binary64)) (sin.f64 kx)) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (-.f64 (fma.f64 (+.f64 (fma.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (-.f64 (fma.f64 (+.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))) (sin.f64 kx) (-.f64 (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 (*.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 ky ky)) #s(literal 1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 ky ky) #s(literal 1/120 binary64)) ky) ky) #s(literal 1/6 binary64)) ky)
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) ky) ky) #s(literal 1/3 binary64)) (*.f64 ky ky))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 (*.f64 (sin.f64 ky) th) th) #s(literal -1/6 binary64) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 (*.f64 (sin.f64 ky) th) th) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 (*.f64 (sin.f64 ky) th) th) #s(literal -1/6 binary64) (sin.f64 ky)) (*.f64 (pow.f64 th #s(literal 4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) th) #s(literal -1/5040 binary64)))))) th)

rewrite217.0ms (1.7%)

Memory
-13.6MiB live, 320.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01349
02249
15949
231949
3312949
0893734
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
6 → 384
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Outputs
(*.f64 (pow.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (-.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (+.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (neg.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (/.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (pow.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
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(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 kx) (neg.f64 kx))) (cos.f64 (+.f64 (neg.f64 kx) (neg.f64 kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 kx) (+.f64 kx (PI.f64)))) (cos.f64 (+.f64 (neg.f64 kx) (+.f64 kx (PI.f64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 kx (PI.f64)) (neg.f64 kx))) (cos.f64 (+.f64 (+.f64 kx (PI.f64)) (neg.f64 kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 kx (PI.f64)) (+.f64 kx (PI.f64)))) (cos.f64 (+.f64 (+.f64 kx (PI.f64)) (+.f64 kx (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 kx) (cos.f64 kx)))
(/.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (-.f64 (*.f64 (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal -2 binary64))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(neg.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(fma.f64 #s(literal 2 binary64) (*.f64 (sinh.f64 (log.f64 (sin.f64 kx))) (cosh.f64 (log.f64 (sin.f64 kx)))) (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 kx) (cos.f64 kx)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (neg.f64 kx)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(fabs.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(fabs.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 kx))))
(exp.f64 (*.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1 binary64))))
(+.f64 (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))

eval134.0ms (1%)

Memory
6.8MiB live, 142.3MiB allocated
Compiler

Compiled 12 601 to 2 762 computations (78.1% saved)

prune85.0ms (0.7%)

Memory
-53.5MiB live, 112.4MiB allocated
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New46221483
Fresh000
Picked101
Done000
Total46321484
Accuracy
100.0%
Counts
484 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.8%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
74.0%
(*.f64 (/.f64 (*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
44.6%
(*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.5%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
76.6%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 2 binary64)) (sin.f64 ky))) (sin.f64 th))
▶99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
▶84.6%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
▶50.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
84.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 kx) (cos.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶85.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
53.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
33.7%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
35.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
80.3%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
80.3%
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
25.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
32.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
93.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
44.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
91.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
▶32.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Compiler

Compiled 894 to 678 computations (24.2% saved)

simplify112.0ms (0.9%)

Memory
-15.1MiB live, 174.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))))
cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
cost-diff3
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
cost-diff5
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
cost-diff0
(sin.f64 ky)
cost-diff0
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff1
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
cost-diff0
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
cost-diff0
(sin.f64 ky)
cost-diff0
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
cost-diff0
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
cost-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))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045331
078296
1138296
2331296
3921296
42361296
55862296
08128291
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(*.f64 ky ky)
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
#s(literal 1 binary64)
(*.f64 (cos.f64 ky) (cos.f64 ky))
(cos.f64 ky)
(sin.f64 th)
th
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
(fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(*.f64 ky ky)
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))
(+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 1 binary64)
(*.f64 (cos.f64 ky) (cos.f64 ky))
(cos.f64 ky)
(sin.f64 th)
th

localize285.0ms (2.2%)

Memory
18.4MiB live, 349.4MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.2109375
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy0.265625
(*.f64 (cos.f64 ky) (cos.f64 ky))
accuracy3.778950357878138
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
accuracy15.169704792627128
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
accuracy0.171875
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
accuracy0.28353500976844204
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy3.778950357878138
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy15.618940236682636
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
accuracy0.171875
(*.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))
accuracy0.2109375
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy3.778950357878138
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
accuracy28.885080322361958
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
accuracy0.0
(sin.f64 th)
accuracy43.18150925353002
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy0.0
(sin.f64 kx)
accuracy0.0625
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.15072250976844204
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy0.171875
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Samples
132.0ms115×2valid
67.0ms84×1valid
22.0ms57×0valid
Compiler

Compiled 331 to 36 computations (89.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 180.0ms
ival-cos: 46.0ms (25.5% of total)
ival-sqrt: 33.0ms (18.3% of total)
ival-sin: 24.0ms (13.3% of total)
ival-mult: 20.0ms (11.1% of total)
adjust: 17.0ms (9.4% of total)
ival-div: 11.0ms (6.1% of total)
ival-hypot: 8.0ms (4.4% of total)
ival-add: 8.0ms (4.4% of total)
ival-pow2: 8.0ms (4.4% of total)
ival-sub: 5.0ms (2.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series65.0ms (0.5%)

Memory
5.7MiB live, 96.0MiB allocated
Counts
22 → 97
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))))
(sin.f64 kx)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(*.f64 (cos.f64 ky) (cos.f64 ky))
Outputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(sqrt (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(sin kx)
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(- 1 (pow (cos ky) 2))
(pow (sin ky) 2)
(pow (cos ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
Calls

9 calls:

TimeVariablePointExpression
12.0ms
ky
@-inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (- 1 (* (cos ky) (cos ky))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (* (cos ky) (cos ky)))
8.0ms
kx
@-inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (- 1 (* (cos ky) (cos ky))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (* (cos ky) (cos ky)))
8.0ms
th
@0
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (- 1 (* (cos ky) (cos ky))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (* (cos ky) (cos ky)))
7.0ms
ky
@0
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (- 1 (* (cos ky) (cos ky))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (* (cos ky) (cos ky)))
6.0ms
kx
@inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1/2 (* (cos (* 2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (- 1 (* (cos ky) (cos ky))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (pow (sin ky) 2) (* (cos ky) (cos ky)))

simplify181.0ms (1.4%)

Memory
25.2MiB live, 214.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06393996
123573632
091003466
Stop Event
1×iter limit
1×node limit
Counts
97 → 94
Calls
Call 1
Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(sqrt (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(sin kx)
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(- 1 (pow (cos ky) 2))
(pow (sin ky) 2)
(pow (cos ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
Outputs
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (*.f64 (*.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)))) (*.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (-.f64 (*.f64 (*.f64 (*.f64 kx kx) #s(literal 1/2 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(+ 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 (*.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (/.f64 (*.f64 kx kx) (sin.f64 ky)) #s(literal 1/2 binary64) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
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(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)
(* (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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(sqrt (- 1 (pow (cos ky) 2)))
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
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(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
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(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(fma.f64 (*.f64 (*.f64 kx kx) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 ky)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 3 binary64)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
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(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
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(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(fma.f64 (*.f64 (*.f64 kx kx) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 3 binary64)))) (sin.f64 ky)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky)))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
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(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
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kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
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(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(fma.f64 (*.f64 kx (*.f64 kx kx)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 kx kx) #s(literal 1/120 binary64)) kx) kx) #s(literal 1/6 binary64)) kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(- 1/2 (* 1/2 (cos (* 2 kx))))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(sqrt (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
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(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
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(sin kx)
(sin.f64 kx)
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt.f64 (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(*.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
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(/ 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))))
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(* 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))))
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(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
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ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
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(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (*.f64 ky (*.f64 ky ky)) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) ky) ky) #s(literal 1/6 binary64)) ky)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal 1/2 binary64) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64)) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 ky ky)) (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
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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)))))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) #s(literal 1/120 binary64)) (sin.f64 th) (fma.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) (sin.f64 th)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) #s(literal 1/2 binary64)))) (*.f64 ky ky) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))) ky)
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
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(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
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(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) ky) ky)
(* (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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(sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))
(fma.f64 (*.f64 (*.f64 ky ky) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))) (*.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
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(+ 1 (* -1 (pow ky 2)))
(fma.f64 (neg.f64 ky) ky #s(literal 1 binary64))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/3 binary64)) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -2/45 binary64) (*.f64 ky ky) #s(literal 1/3 binary64)) ky) ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(- 1 (pow (cos 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 (cos ky) 2)
(pow.f64 (cos.f64 ky) #s(literal 2 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
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th
(* th (+ 1 (* -1/6 (pow th 2))))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
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(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(fma.f64 (*.f64 th (*.f64 th th)) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) th) th) #s(literal 1/6 binary64)) th)
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
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(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky)) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th)))))) th)

rewrite144.0ms (1.1%)

Memory
-8.2MiB live, 188.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045235
078171
1261171
21968171
08146171
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 818
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky))))))
(sin.f64 kx)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(*.f64 (cos.f64 ky) (cos.f64 ky))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (sin.f64 th) (sin.f64 ky)))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (neg.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(exp.f64 (-.f64 (log.f64 (sin.f64 ky)) (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (sin.f64 ky))) (neg.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (fabs.f64 (sqrt.f64 (sin.f64 ky))) (fabs.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky))))
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (cos.f64 ky) #s(literal 4 binary64)) (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (cos.f64 ky) (cos.f64 ky) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 4 binary64))) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 (cos.f64 ky) (cos.f64 ky) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 4 binary64))) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (cos.f64 ky))
(sin.f64 (acos.f64 (neg.f64 (neg.f64 (cos.f64 ky)))))
(sin.f64 (acos.f64 (neg.f64 (cos.f64 ky))))
(sin.f64 (acos.f64 (cos.f64 ky)))
(sin.f64 ky)
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (sin.f64 ky))))
(fabs.f64 (neg.f64 (sin.f64 ky)))
(fabs.f64 (sin.f64 ky))
(cos.f64 (asin.f64 (neg.f64 (neg.f64 (cos.f64 ky)))))
(cos.f64 (asin.f64 (neg.f64 (cos.f64 ky))))
(cos.f64 (asin.f64 (cos.f64 ky)))
(exp.f64 (/.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sin.f64 ky)))
(+.f64 (cosh.f64 (log.f64 (sin.f64 ky))) (sinh.f64 (log.f64 (sin.f64 ky))))
(*.f64 (neg.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1 binary64)) #s(literal 2 binary64)) (pow.f64 (cos.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (+.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (cos.f64 ky) #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 (pow.f64 (cos.f64 ky) #s(literal 4 binary64)) (*.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))))
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(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))
(+.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 ky))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (neg.f64 ky) (PI.f64))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) ky) (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (neg.f64 ky))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))

eval184.0ms (1.4%)

Memory
-16.1MiB live, 212.7MiB allocated
Compiler

Compiled 23 860 to 4 175 computations (82.5% saved)

prune49.0ms (0.4%)

Memory
22.0MiB live, 122.7MiB allocated
Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New78323806
Fresh61016
Picked415
Done000
Total79334827
Accuracy
100.0%
Counts
827 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.8%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
80.2%
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
74.0%
(*.f64 (/.f64 (*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
44.6%
(*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
▶99.5%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
▶50.1%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
55.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
75.8%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
75.5%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
35.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
24.1%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
27.9%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
84.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
35.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
41.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶34.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
48.1%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
80.3%
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
49.9%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))))
25.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
32.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
41.3%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
75.6%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 ky))) (sin.f64 th))
30.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
44.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
91.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
✓32.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
18.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
▶19.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
41.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
38.8%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
▶75.5%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
30.1%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
30.0%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
Compiler

Compiled 1 781 to 1 351 computations (24.1% saved)

simplify173.0ms (1.3%)

Memory
-6.5MiB live, 143.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
cost-diff1
(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
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))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
cost-diff2
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
cost-diff0
(sin.f64 ky)
cost-diff0
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
cost-diff0
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
cost-diff1
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
cost-diff0
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
cost-diff0
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
cost-diff2
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
cost-diff0
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
cost-diff0
(sin.f64 th)
cost-diff0
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff0
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053425
085420
1157420
2355420
3720414
41599414
53678414
67320414
08226394
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 th)
th
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 ky)
ky
(sin.f64 kx)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 th th)
th
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
(sin.f64 ky)
ky
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal -2 binary64) kx)
#s(literal -2 binary64)
kx
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 th th)
th
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))
(sin.f64 ky)
ky
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal -2 binary64) kx)
#s(literal -2 binary64)
kx
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
Outputs
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 th)
th
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
ky
(sin.f64 kx)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))
(*.f64 th th)
th
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))))
(sin.f64 ky)
ky
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))
(*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal -2 binary64) kx)
#s(literal -2 binary64)
kx
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64))
(*.f64 th th)
th
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))
(sin.f64 ky)
ky
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))
(*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal -2 binary64) kx)
#s(literal -2 binary64)
kx
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th

localize301.0ms (2.3%)

Memory
-18.6MiB live, 548.6MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.23046875
(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy2.786987787896687
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
accuracy4.14502541952607
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
accuracy11.571630098611738
(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
accuracy0.15072250976844204
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy0.171875
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy0.3254530277145722
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy31.846516420147786
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy0.171875
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
accuracy14.98082558484357
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
accuracy15.618940236682636
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
accuracy33.94844393629097
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
accuracy0.078125
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
accuracy0.3254530277145722
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy31.846516420147786
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy43.18150925353002
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy0.0
(sin.f64 kx)
accuracy0.0625
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.25
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy0.28744125976844204
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
Samples
113.0ms79×2valid
69.0ms128×0valid
28.0ms15×3valid
26.0ms34×1valid
Compiler

Compiled 386 to 48 computations (87.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 186.0ms
ival-cos: 43.0ms (23.2% of total)
ival-mult: 35.0ms (18.9% of total)
ival-sin: 24.0ms (12.9% of total)
adjust: 16.0ms (8.6% of total)
ival-div: 16.0ms (8.6% of total)
ival-sqrt: 12.0ms (6.5% of total)
ival-pow2: 11.0ms (5.9% of total)
ival-add: 10.0ms (5.4% of total)
ival-sub: 7.0ms (3.8% of total)
ival-hypot: 7.0ms (3.8% of total)
const: 5.0ms (2.7% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series54.0ms (0.4%)

Memory
3.5MiB live, 139.0MiB allocated
Counts
22 → 122
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 th)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
(sin.f64 ky)
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(sin.f64 kx)
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(*.f64 (sin.f64 th) (sin.f64 ky))
Outputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ (sin th) (sin ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(- 1/2 (* 1/2 (cos (* -2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
(sin kx)
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (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 kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))))))))
(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(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)))))))))))))
(* 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))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))))
(* th (sin ky))
(* 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))))))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (pow th 2))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
Calls

9 calls:

TimeVariablePointExpression
12.0ms
ky
@0
((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin kx) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt (- 1/2 (* (cos (* -2 kx)) 1/2))) (* (sin th) (sin ky)))
7.0ms
th
@inf
((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin kx) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt (- 1/2 (* (cos (* -2 kx)) 1/2))) (* (sin th) (sin ky)))
5.0ms
ky
@inf
((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin kx) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt (- 1/2 (* (cos (* -2 kx)) 1/2))) (* (sin th) (sin ky)))
5.0ms
ky
@-inf
((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin kx) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt (- 1/2 (* (cos (* -2 kx)) 1/2))) (* (sin th) (sin ky)))
5.0ms
th
@-inf
((* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (- 1/2 (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sin kx) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt (- 1/2 (* (cos (* -2 kx)) 1/2))) (* (sin th) (sin ky)))

simplify140.0ms (1.1%)

Memory
35.1MiB live, 235.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07334976
127294669
082254319
Stop Event
1×iter limit
1×node limit
Counts
122 → 119
Calls
Call 1
Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ (sin th) (sin ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(- 1/2 (* 1/2 (cos (* -2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
(sin kx)
(sqrt (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))
(sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (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 kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))))))))
(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(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)))))))))))))
(* 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))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))))
(* th (sin ky))
(* 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))))))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (pow th 2))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
Outputs
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)))) (*.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
(/ (sin th) (sin ky))
(/.f64 (sin.f64 th) (sin.f64 ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (sin.f64 th) (sin.f64 ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sin.f64 th)) (sin.f64 ky)) (*.f64 kx kx)))) (*.f64 kx kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (sin.f64 ky)) (*.f64 kx kx)) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sin.f64 th)) (sin.f64 ky)))) (*.f64 kx kx) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (*.f64 kx kx) (/.f64 (sin.f64 th) (sin.f64 ky)))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 kx kx)) #s(literal 1/2 binary64)) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2/45 binary64)) (*.f64 kx kx)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 ky)) (*.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 ky))
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(+ (pow kx 2) (pow (sin ky) 2))
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(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
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(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
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kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
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(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(- 1/2 (* 1/2 (cos (* -2 kx))))
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(sin kx)
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(/ (* ky (sin th)) (sin kx))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
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(/ (sin th) (sin kx))
(/.f64 (sin.f64 th) (sin.f64 kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
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(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
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(+ (* (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)))
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(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
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(+ (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))))))
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(* (* ky (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))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
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(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
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ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
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(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
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(/ 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))))
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(* 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))))
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(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
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(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
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(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
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(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
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(* (* ky (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))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))))))))
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(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
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(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
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(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
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(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
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(sqrt (- 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))))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 ky ky)) #s(literal 1/2 binary64))) (*.f64 ky ky) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal 2/45 binary64)) (*.f64 ky ky)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)))) (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))) (*.f64 ky ky) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 ky ky) (sin.f64 th)) ky)
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 ky ky) (*.f64 #s(literal -1/6 binary64) (sin.f64 th))) (*.f64 ky ky) (sin.f64 th)) ky)
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1/6 binary64))) (*.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 th th) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 th th) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (sin ky))
(*.f64 (sin.f64 ky) th)
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 th th) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky))) (*.f64 th th) (sin.f64 ky)) th)
(* -1/6 (pow th 3))
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(* -1/6 (pow th 2))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th)))) (pow.f64 th #s(literal 3 binary64)))

rewrite211.0ms (1.6%)

Memory
-24.5MiB live, 265.5MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
053308
085260
1308207
22176204
08957204
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
22 → 489
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 th)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))))
(sin.f64 ky)
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(sin.f64 kx)
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(*.f64 (sin.f64 th) (sin.f64 ky))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (neg.f64 (sin.f64 th)) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 th))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (neg.f64 (neg.f64 (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (sin.f64 th) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(sin.f64 th)
(*.f64 (neg.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64) (*.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 (*.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) #s(literal 2 binary64) (*.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 (*.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))) #s(literal 2 binary64))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 ky) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))))
(/.f64 (*.f64 (hypot.f64 (sin.f64 ky) (cos.f64 kx)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (cos.f64 kx)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (sin.f64 ky))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (sin.f64 kx))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)) (sin.f64 ky))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)) (sin.f64 kx))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(hypot.f64 (sin.f64 kx) (pow.f64 (neg.f64 (neg.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
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(pow.f64 (sin.f64 kx) #s(literal 1 binary64))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (fabs.f64 (cos.f64 kx)))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (sqrt.f64 (neg.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 kx)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (fabs.f64 (cos.f64 kx)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(sin.f64 kx)
(sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (sin.f64 kx))))
(fabs.f64 (neg.f64 (sin.f64 kx)))
(fabs.f64 (sin.f64 kx))
(exp.f64 (/.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (sin.f64 kx)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(+.f64 (cosh.f64 (log.f64 (sin.f64 kx))) (sinh.f64 (log.f64 (sin.f64 kx))))
#s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))
(*.f64 (neg.f64 (sqrt.f64 (sin.f64 kx))) (neg.f64 (sqrt.f64 (sin.f64 kx))))
(*.f64 (fabs.f64 (sqrt.f64 (sin.f64 kx))) (fabs.f64 (sqrt.f64 (sin.f64 kx))))
(*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 kx)))) (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(*.f64 (sqrt.f64 (neg.f64 (sin.f64 kx))) (sqrt.f64 (neg.f64 (sin.f64 kx))))
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sin.f64 kx)) (sqrt.f64 (sin.f64 kx)))
(pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sin.f64 kx)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 1 binary64))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (fabs.f64 (cos.f64 kx)))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64))))) (sqrt.f64 (neg.f64 (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 kx)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (fabs.f64 (cos.f64 kx)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(sin.f64 kx)
(sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (sin.f64 kx))))
(fabs.f64 (neg.f64 (sin.f64 kx)))
(fabs.f64 (sin.f64 kx))
(exp.f64 (/.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (sin.f64 kx)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(+.f64 (cosh.f64 (log.f64 (sin.f64 kx))) (sinh.f64 (log.f64 (sin.f64 kx))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) #s(literal 2 binary64))
(-.f64 (/.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 ky th)) #s(literal 2 binary64)))

eval167.0ms (1.3%)

Memory
14.5MiB live, 290.9MiB allocated
Compiler

Compiled 37 173 to 3 976 computations (89.3% saved)

prune136.0ms (1.1%)

Memory
-14.3MiB live, 140.5MiB allocated
Pruning

53 alts after pruning (51 fresh and 2 done)

PrunedKeptTotal
New89537932
Fresh141428
Picked415
Done011
Total91353966
Accuracy
100.0%
Counts
966 → 53
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶95.8%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
32.7%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
46.2%
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
80.2%
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
31.9%
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
10.9%
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
44.6%
(*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
38.0%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))))
54.4%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
75.7%
(*.f64 (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 ky))
38.9%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
✓50.1%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
33.6%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
27.8%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
38.6%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
75.8%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
38.5%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
75.5%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
35.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
41.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
16.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
34.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
33.9%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
16.7%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
33.2%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
19.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
48.1%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
29.8%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
80.3%
(*.f64 (sqrt.f64 (sin.f64 ky)) (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
35.1%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
25.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
32.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
▶30.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
18.2%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
✓32.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
18.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
18.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
19.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
▶8.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
8.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
8.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
41.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
90.9%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (pow.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky))))
95.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
38.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
▶38.8%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
30.1%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
75.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
▶32.2%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
37.2%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
33.9%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
30.0%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
Compiler

Compiled 3 225 to 2 446 computations (24.2% saved)

simplify202.0ms (1.6%)

Memory
14.6MiB live, 156.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 ky)
cost-diff0
(*.f64 (sin.f64 ky) th)
cost-diff0
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
cost-diff0
(/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)
cost-diff0
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky))
cost-diff0
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
cost-diff0
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)
cost-diff0
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th 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) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
cost-diff0
(sin.f64 ky)
cost-diff0
(sin.f64 th)
cost-diff0
(*.f64 (sin.f64 th) (sin.f64 ky))
cost-diff0
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069567
0106562
1189553
2417553
3817553
41561553
53431553
67004553
08434549
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(*.f64 th th)
th
#s(literal -1/6 binary64)
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
#s(literal 1/2 binary64)
ky
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
#s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(fma.f64 ky ky #s(literal 1/2 binary64))
ky
#s(literal 1/2 binary64)
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) th)
(sin.f64 ky)
ky
th
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
Outputs
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(*.f64 th th)
th
#s(literal -1/6 binary64)
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky))
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
(fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
#s(literal 1/2 binary64)
ky
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 ky ky #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 ky ky #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
#s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))
#s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 ky ky #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 ky ky #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(fma.f64 ky ky #s(literal 1/2 binary64))
ky
#s(literal 1/2 binary64)
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) th)))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) th))
(*.f64 (sin.f64 ky) th)
(sin.f64 ky)
ky
th
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
(fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

localize728.0ms (5.7%)

Memory
17.9MiB live, 440.4MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy2.7228665476651286
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
accuracy4.14502541952607
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
accuracy11.571630098611738
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
accuracy31.589200026748813
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
accuracy2.786987787896687
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
accuracy4.14502541952607
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))))
accuracy11.196701807517812
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))
accuracy28.670466400915377
#s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))
accuracy0.23828125
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)
accuracy15.470570421015575
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
accuracy15.618940236682636
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
accuracy36.71652967042382
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky))
accuracy0.4348280277145722
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
accuracy30.671799455577666
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
accuracy31.846516420147786
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))
accuracy43.18150925353002
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
accuracy0.0
(sin.f64 kx)
accuracy0.0625
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.23046875
(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy2.758022797665128
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Samples
239.0ms128×0valid
199.0ms79×2valid
75.0ms15×3valid
57.0ms34×1valid
Compiler

Compiled 431 to 57 computations (86.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 446.0ms
ival-cos: 237.0ms (53.1% of total)
ival-mult: 72.0ms (16.1% of total)
adjust: 47.0ms (10.5% of total)
ival-sin: 22.0ms (4.9% of total)
ival-add: 16.0ms (3.6% of total)
ival-sqrt: 15.0ms (3.4% of total)
ival-div: 14.0ms (3.1% of total)
ival-pow2: 7.0ms (1.6% of total)
ival-hypot: 6.0ms (1.3% of total)
const: 5.0ms (1.1% of total)
ival-sub: 4.0ms (0.9% of total)
exact: 1.0ms (0.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series163.0ms (1.3%)

Memory
-24.7MiB live, 83.8MiB allocated
Counts
27 → 143
Calls
Call 1
Inputs
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) th)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
#s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
Outputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(/ ky kx)
(/ (+ ky (* 1/6 (* (pow kx 2) ky))) kx)
(/ (+ ky (* (pow kx 2) (+ (* 7/360 (* (pow kx 2) ky)) (* 1/6 ky)))) kx)
(/ (+ ky (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* 31/15120 (* (pow kx 2) ky)) (* 7/360 ky)))))) kx)
(/ 1 kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(/ 1 (pow (sin ky) 2))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6)))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6))))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(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))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(pow ky 2)
(+ (pow kx 2) (pow ky 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow ky 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow ky 2))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* ky (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
(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)))))))
(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
(/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow ky 2)))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(* (* ky (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)))))))))))))))))))))
(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))
(+ (* -1 (/ (pow ky 2) (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(* (* ky th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
(* ky (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* 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 (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* 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 (* (* 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 (* (* 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 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky th)
(* ky (+ th (* -1/6 (* (pow ky 2) th))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* 1/120 (* (pow ky 2) th))))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) th)) (* 1/120 th)))))))
(+ (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))))))
(- 1/2 (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))))))))))
(* (sin ky) (sin th))
(* th (sin ky))
(* (pow ky 2) (+ 1 (+ (* -1/2 (/ (cos (* 2 kx)) (pow ky 2))) (* 1/2 (/ 1 (pow ky 2))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 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))))))))))))))
(* -1/6 (pow th 2))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
Calls

9 calls:

TimeVariablePointExpression
24.0ms
ky
@-inf
((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (* (sin ky) th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin kx) (* (* th th) -1/6) (+ (* -1/2 (cos (* 2 kx))) 1/2) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)))))
10.0ms
ky
@0
((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (* (sin ky) th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin kx) (* (* th th) -1/6) (+ (* -1/2 (cos (* 2 kx))) 1/2) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)))))
7.0ms
ky
@inf
((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (* (sin ky) th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin kx) (* (* th th) -1/6) (+ (* -1/2 (cos (* 2 kx))) 1/2) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)))))
6.0ms
kx
@inf
((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (* (sin ky) th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin kx) (* (* th th) -1/6) (+ (* -1/2 (cos (* 2 kx))) 1/2) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)))))
6.0ms
th
@-inf
((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2))) (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (* (sin ky) th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin kx) (* (* th th) -1/6) (+ (* -1/2 (cos (* 2 kx))) 1/2) (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)))))

simplify196.0ms (1.5%)

Memory
22.1MiB live, 239.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08245619
131445343
087534907
Stop Event
1×iter limit
1×node limit
Counts
143 → 140
Calls
Call 1
Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(/ ky kx)
(/ (+ ky (* 1/6 (* (pow kx 2) ky))) kx)
(/ (+ ky (* (pow kx 2) (+ (* 7/360 (* (pow kx 2) ky)) (* 1/6 ky)))) kx)
(/ (+ ky (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* 31/15120 (* (pow kx 2) ky)) (* 7/360 ky)))))) kx)
(/ 1 kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(/ 1 (pow (sin ky) 2))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6)))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6))))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(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))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(pow ky 2)
(+ (pow kx 2) (pow ky 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow ky 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow ky 2))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* ky (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
(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)))))))
(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
(/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow ky 2)))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))
(sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
(* (* ky (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)))))))))))))))))))))
(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))
(+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))))))))
(/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))
(+ (* -1 (/ (pow ky 2) (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2)))) (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
(* (* ky th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
(* ky (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* 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 (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* 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 (* (* 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 (* (* 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 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky th)
(* ky (+ th (* -1/6 (* (pow ky 2) th))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* 1/120 (* (pow ky 2) th))))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) th)) (* 1/120 th)))))))
(+ (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))))))
(- 1/2 (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (pow ky 2)) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))) (* 1/2 (cos (* -2 kx))))
(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))))))))))
(* (sin ky) (sin th))
(* th (sin ky))
(* (pow ky 2) (+ 1 (+ (* -1/2 (/ (cos (* 2 kx)) (pow ky 2))) (* 1/2 (/ 1 (pow ky 2))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 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))))))))))))))
(* -1/6 (pow th 2))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
Outputs
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 (*.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)))) (*.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))
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(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
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(/ ky kx)
(/.f64 ky kx)
(/ (+ ky (* 1/6 (* (pow kx 2) ky))) kx)
(/.f64 (fma.f64 (*.f64 (*.f64 kx kx) ky) #s(literal 1/6 binary64) ky) kx)
(/ (+ ky (* (pow kx 2) (+ (* 7/360 (* (pow kx 2) ky)) (* 1/6 ky)))) kx)
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(/ (+ ky (* (pow kx 2) (+ (* 1/6 ky) (* (pow kx 2) (+ (* 31/15120 (* (pow kx 2) ky)) (* 7/360 ky)))))) kx)
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(/ 1 kx)
(/.f64 #s(literal 1 binary64) kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
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(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
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(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
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(/ 1 (sin ky))
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(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
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(/ 1 (pow (sin ky) 2))
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th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
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(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
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(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (/.f64 (*.f64 kx kx) (sin.f64 ky)) #s(literal 1/2 binary64) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
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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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kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(*.f64 (fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
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(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
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(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
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(pow (sin ky) 2)
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(+ (pow kx 2) (pow (sin ky) 2))
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(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
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(pow ky 2)
(*.f64 ky ky)
(+ (pow kx 2) (pow ky 2))
(fma.f64 kx kx (*.f64 ky ky))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow ky 2))
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(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow ky 2))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
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(* ky (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
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(sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))
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(sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))
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(/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))
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(* ky (sin th))
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ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
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(* (* ky (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))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx)))))))))))))))
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(* ky (+ (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 4))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (sqrt (- 1/2 (* 1/2 (cos (* 2 kx))))))) (+ (* -1/240 (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (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))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))
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(* ky (+ (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3)))) (- 1/2 (* 1/2 (cos (* -2 kx)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 4)))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* -2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* -2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx)))))))))))))))))))))
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(sqrt (/ 1 (- 1/2 (* 1/2 (cos (* -2 kx))))))
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(* (* ky th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
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(* ky (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))))
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(* ky (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* 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 (+ (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* 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 (* (* 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 (* (* 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 (* th (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* th (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))))))))))))
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(- (+ 1/2 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))) (* 1/2 (cos (* -2 kx))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64)))
(+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64)))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* -1/2 (* (pow ky 2) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 ky ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #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 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))
(fma.f64 (*.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 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (*.f64 (*.f64 ky ky) (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))))) (*.f64 ky ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))) (*.f64 ky ky)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))))) (*.f64 ky ky) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64))) (*.f64 ky ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* th (sin ky))
(*.f64 (sin.f64 ky) th)
(* (pow ky 2) (+ 1 (+ (* -1/2 (/ (cos (* 2 kx)) (pow ky 2))) (* 1/2 (/ 1 (pow ky 2))))))
(*.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)) (*.f64 ky ky)) #s(literal 1 binary64)) (*.f64 ky ky))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(*.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 th th) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky))) (*.f64 th th) (sin.f64 ky)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* 2 kx))))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 th th) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin ky) 2)) (* 1/2 (cos (* -2 kx))))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (*.f64 th th) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))) (*.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) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* -1/6 (pow th 2))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(* -1/6 (pow th 3))
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 th th)))) (pow.f64 th #s(literal 3 binary64)))

rewrite364.0ms (2.8%)

Memory
41.8MiB live, 444.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069471
0106430
1378345
22713341
010805331
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
27 → 602
Calls
Call 1
Inputs
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))))
(*.f64 (sin.f64 ky) th)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))
#s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 ky th)) (cos.f64 (+.f64 ky th))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) #s(literal 2 binary64))
(-.f64 (/.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 ky th)) #s(literal 2 binary64)))
(sin.f64 th)
(*.f64 (neg.f64 (sqrt.f64 (sin.f64 ky))) (neg.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (fabs.f64 (sqrt.f64 (sin.f64 ky))) (fabs.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 ky)))) (sqrt.f64 (neg.f64 (neg.f64 (sin.f64 ky)))))
(*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky))))
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) (sqrt.f64 #s(literal -2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))
(sin.f64 ky)
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 (sin.f64 ky))))
(fabs.f64 (neg.f64 (sin.f64 ky)))
(fabs.f64 (sin.f64 ky))
(exp.f64 (/.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sin.f64 ky)))
(+.f64 (cosh.f64 (log.f64 (sin.f64 ky))) (sinh.f64 (log.f64 (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))
(*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)
(*.f64 th #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))))
#s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky)))
#s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky))
(*.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) ky)
(*.f64 ky (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) ky) (sin.f64 kx))
(/.f64 (*.f64 ky #s(literal 1 binary64)) (sin.f64 kx))
(*.f64 (neg.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/4 binary64))))))
(*.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64))))
(*.f64 (pow.f64 (+.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sin.f64 kx) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/4 binary64))))))
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(pow.f64 (*.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64)) (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 kx) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) (sin.f64 kx))
(sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64)))
(fabs.f64 (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))
(exp.f64 (/.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (*.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (sin.f64 ky)) (sin.f64 th))
(*.f64 (*.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (sin.f64 th)) (sin.f64 ky))
(*.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (*.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (sin.f64 th)))
(*.f64 (sin.f64 th) (*.f64 (sin.f64 ky) (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sin.f64 ky) (sin.f64 th))) (sqrt.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/.f64 (*.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(/.f64 (*.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(literal 1 binary64)) (sqrt.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th)))) (*.f64 (sqrt.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 2 binary64)))
(/.f64 (*.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 ky th))) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(*.f64 (neg.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (neg.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 ky ky (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
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(+.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (*.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64))))
(+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 (neg.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64))) (sqrt.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))))
(*.f64 (sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal -1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)))
(fabs.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(exp.f64 (/.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))))

eval296.0ms (2.3%)

Memory
-31.1MiB live, 452.0MiB allocated
Compiler

Compiled 44 664 to 4 655 computations (89.6% saved)

prune96.0ms (0.7%)

Memory
14.0MiB live, 293.6MiB allocated
Pruning

67 alts after pruning (64 fresh and 3 done)

PrunedKeptTotal
New86029889
Fresh113546
Picked325
Done112
Total87567942
Accuracy
100.0%
Counts
942 → 67
Alt Table
Click to see full alt table
StatusAccuracyProgram
76.4%
(/.f64 (*.f64 (sin.f64 th) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
75.7%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64)))
75.5%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))))
32.7%
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
50.6%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
31.9%
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
10.9%
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
75.7%
(*.f64 (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 ky))
38.9%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
33.6%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
27.8%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
38.6%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
75.8%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
38.5%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
41.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
16.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
34.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
33.9%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
16.7%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
33.2%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
19.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
48.1%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
29.8%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
35.1%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
25.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
32.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
39.2%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)) ky)) (sin.f64 th))
19.9%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
38.2%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
✓30.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
15.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
17.6%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
16.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
17.6%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
27.5%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
15.9%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
21.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
21.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
18.2%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
30.0%
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
✓32.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
18.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
18.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
19.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
✓8.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
8.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
8.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
8.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
41.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
46.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
95.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
24.8%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
38.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
46.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
16.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
38.8%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
16.9%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
16.4%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
30.1%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
75.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
37.6%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
33.9%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
13.9%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
37.2%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
15.3%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
15.1%
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
Compiler

Compiled 5 979 to 2 347 computations (60.7% saved)

regimes342.0ms (2.7%)

Memory
1.3MiB live, 613.7MiB allocated
Counts
111 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
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(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (+.f64 (cosh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal -2 binary64))) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
(*.f64 (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(*.f64 (/.f64 (*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64)) #s(literal 2 binary64))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Calls

9 calls:

58.0ms
(sin.f64 th)
51.0ms
(*.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))
48.0ms
(sin.f64 ky)
35.0ms
(sin.f64 kx)
31.0ms
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 42 to 51 computations (-21.4% saved)

regimes303.0ms (2.3%)

Memory
19.1MiB live, 352.4MiB allocated
Counts
85 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)) ky)) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64)))
Calls

9 calls:

101.0ms
th
29.0ms
ky
27.0ms
kx
25.0ms
(sin.f64 th)
25.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
93.5%2kx
99.3%2ky
87.2%2th
80.3%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))
99.6%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)))))
99.3%3(sin.f64 ky)
93.5%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
93.5%3(sin.f64 kx)
87.2%3(sin.f64 th)
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes28.0ms (0.2%)

Memory
2.5MiB live, 47.7MiB allocated
Counts
80 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 ky))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
Calls

1 calls:

23.0ms
ky
Results
AccuracySegmentsBranch
99.3%2ky
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes28.0ms (0.2%)

Memory
-5.9MiB live, 47.4MiB allocated
Counts
78 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
Calls

1 calls:

24.0ms
ky
Results
AccuracySegmentsBranch
99.3%2ky
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes229.0ms (1.8%)

Memory
15.7MiB live, 439.7MiB allocated
Counts
76 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
Calls

8 calls:

49.0ms
(sin.f64 ky)
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)))))
25.0ms
(sin.f64 kx)
24.0ms
th
22.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
77.8%3(sin.f64 th)
77.9%2th
77.4%3(sin.f64 kx)
77.3%2kx
77.3%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
90.0%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)))))
83.7%3(sin.f64 ky)
83.7%2ky
Compiler

Compiled 26 to 38 computations (-46.2% saved)

regimes21.0ms (0.2%)

Memory
4.9MiB live, 50.3MiB allocated
Counts
67 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
Calls

1 calls:

17.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
90.0%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 13 to 11 computations (15.4% saved)

regimes69.0ms (0.5%)

Memory
17.7MiB live, 63.0MiB allocated
Counts
65 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

2 calls:

48.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
17.0ms
ky
Results
AccuracySegmentsBranch
79.4%2ky
87.0%5(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 14 to 14 computations (0% saved)

regimes141.0ms (1.1%)

Memory
-10.5MiB live, 234.4MiB allocated
Counts
61 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

7 calls:

20.0ms
kx
19.0ms
th
19.0ms
(*.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))
18.0ms
(sin.f64 ky)
16.0ms
ky
Results
AccuracySegmentsBranch
63.6%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
63.5%3kx
73.7%2th
73.6%2ky
63.7%4(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
74.4%3(sin.f64 ky)
80.3%4(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 38 to 43 computations (-13.2% saved)

regimes22.0ms (0.2%)

Memory
-3.2MiB live, 40.4MiB allocated
Counts
60 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

19.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
80.2%4(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes21.0ms (0.2%)

Memory
-7.8MiB live, 37.0MiB allocated
Counts
59 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 (sin.f64 ky) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(literal 1/2 binary64)))))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64))) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal -1 binary64))) ky)) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

17.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
80.2%4(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes98.0ms (0.8%)

Memory
11.2MiB live, 197.0MiB allocated
Counts
52 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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) (sqrt.f64 (+.f64 (pow.f64 #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

6 calls:

20.0ms
(sin.f64 kx)
17.0ms
(sin.f64 ky)
16.0ms
(sin.f64 th)
15.0ms
th
13.0ms
ky
Results
AccuracySegmentsBranch
69.8%3(sin.f64 ky)
65.3%2ky
58.7%2th
63.2%3(sin.f64 kx)
58.6%3(sin.f64 th)
72.6%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 21 to 29 computations (-38.1% saved)

regimes44.0ms (0.3%)

Memory
-10.0MiB live, 91.0MiB allocated
Counts
49 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

3 calls:

15.0ms
ky
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)))))
13.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
51.3%2ky
56.0%3(sin.f64 ky)
67.0%4(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 16 to 18 computations (-12.5% saved)

regimes58.0ms (0.5%)

Memory
-6.6MiB live, 85.3MiB allocated
Counts
48 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (fma.f64 #s(literal 2 binary64) kx (PI.f64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx (PI.f64))))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
Calls

4 calls:

17.0ms
(sin.f64 kx)
13.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
13.0ms
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
63.2%3(sin.f64 kx)
63.2%3kx
63.2%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
62.7%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)))))
Compiler

Compiled 20 to 24 computations (-20% saved)

regimes45.0ms (0.3%)

Memory
18.4MiB live, 64.5MiB allocated
Counts
40 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
Calls

4 calls:

12.0ms
kx
11.0ms
(sin.f64 kx)
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)))))
10.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
61.3%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)))))
61.4%3kx
61.4%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
62.2%3(sin.f64 kx)
Compiler

Compiled 20 to 24 computations (-20% saved)

regimes12.0ms (0.1%)

Memory
14.8MiB live, 14.8MiB allocated
Counts
36 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))
Calls

1 calls:

10.0ms
(sin.f64 kx)
Results
AccuracySegmentsBranch
62.2%3(sin.f64 kx)
Compiler

Compiled 2 to 4 computations (-100% saved)

regimes49.0ms (0.4%)

Memory
-36.6MiB live, 63.4MiB allocated
Counts
35 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 2/45 binary64)) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64))))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (pow.f64 (neg.f64 (sin.f64 kx)) #s(literal -1 binary64)) ky)) (sin.f64 th))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))
Calls

4 calls:

18.0ms
(sin.f64 kx)
10.0ms
kx
10.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
9.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
61.4%3kx
61.4%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
52.5%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))
60.1%3(sin.f64 kx)
Compiler

Compiled 23 to 26 computations (-13% saved)

regimes26.0ms (0.2%)

Memory
-5.6MiB live, 40.7MiB allocated
Counts
29 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64))))) ky)) (sin.f64 th))
Outputs
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
(*.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

3 calls:

8.0ms
kx
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)))))
7.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
60.9%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)))))
59.5%3kx
59.5%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Compiler

Compiled 18 to 20 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory
17.5MiB live, 17.5MiB allocated
Counts
26 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

1 calls:

7.0ms
(/.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
60.9%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes37.0ms (0.3%)

Memory
11.7MiB live, 57.9MiB allocated
Counts
25 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (fma.f64 (*.f64 (*.f64 kx kx) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) #s(approx (+ (* -1/2 (cos (* 2 kx))) (+ (* ky ky) 1/2)) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
Outputs
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

5 calls:

8.0ms
(sin.f64 kx)
7.0ms
kx
7.0ms
th
7.0ms
(/.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)))))
6.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
49.5%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
49.5%2kx
52.6%3(sin.f64 kx)
38.6%4th
57.8%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 21 to 27 computations (-28.6% saved)

regimes15.0ms (0.1%)

Memory
-26.4MiB live, 23.6MiB allocated
Counts
21 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

2 calls:

8.0ms
(sin.f64 th)
6.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
40.6%5(sin.f64 th)
56.4%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 15 to 15 computations (0% saved)

regimes41.0ms (0.3%)

Memory
18.3MiB live, 64.7MiB allocated
Counts
19 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 #s(literal 1 binary64) kx)) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 #s(approx (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 kx kx)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) (+ (* (sin ky) (sin ky)) 1/2))))) (*.f64 (*.f64 ky th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)) #s(literal 1/2 binary64)))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) ky)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* -1/2 (cos (* 2 kx))) 1/2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 2/45 binary64) (*.f64 kx kx)) #s(literal 1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) ky)) (sin.f64 th))
Outputs
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

7 calls:

6.0ms
kx
6.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
6.0ms
(sin.f64 kx)
5.0ms
ky
5.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
41.9%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))
44.6%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
44.5%3kx
44.7%4(sin.f64 kx)
44.3%2ky
44.1%2(sin.f64 ky)
46.6%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 39 to 44 computations (-12.8% saved)

regimes27.0ms (0.2%)

Memory
-0.9MiB live, 45.7MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

7 calls:

8.0ms
(sin.f64 kx)
4.0ms
kx
3.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
3.0ms
(sin.f64 ky)
3.0ms
ky
Results
AccuracySegmentsBranch
37.0%3(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
32.5%1(sin.f64 kx)
34.2%2kx
32.5%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
34.6%2(sin.f64 ky)
34.3%2ky
36.8%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 39 to 44 computations (-12.8% saved)

regimes23.0ms (0.2%)

Memory
-4.7MiB live, 42.2MiB 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) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
Calls

9 calls:

3.0ms
kx
3.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
2.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
2.0ms
(sin.f64 th)
2.0ms
(sin.f64 kx)
Results
AccuracySegmentsBranch
21.3%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
19.1%1(sin.f64 kx)
21.5%2kx
21.3%2ky
21.5%2(sin.f64 ky)
24.2%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))
19.1%1th
19.1%1(sin.f64 th)
23.8%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes5.0ms (0%)

Memory
9.4MiB live, 9.4MiB allocated
Counts
4 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
Calls

2 calls:

2.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
2.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
23.8%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)))))
23.7%2(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 29 to 24 computations (17.2% saved)

regimes15.0ms (0.1%)

Memory
-20.7MiB live, 28.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

9 calls:

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))
1.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
1.0ms
(sin.f64 th)
1.0ms
(sin.f64 ky)
1.0ms
(sin.f64 kx)
Results
AccuracySegmentsBranch
8.6%1(sin.f64 th)
8.6%1(sin.f64 kx)
8.6%1th
8.6%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
8.6%1ky
8.6%1kx
8.6%1(sin.f64 ky)
8.6%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
8.6%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch15.0ms (0.1%)

Memory
22.2MiB live, 22.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
13.0ms
0.0018900373297351366
0.007120298201771899
Samples
10.0ms80×0valid
Compiler

Compiled 244 to 208 computations (14.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-sin: 4.0ms (52.5% of total)
ival-pow2: 2.0ms (26.2% of total)
ival-sqrt: 1.0ms (13.1% of total)
ival-div: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
0.0018900373297351366
0.007120298201771899
Compiler

Compiled 244 to 208 computations (14.8% saved)

bsearch1.0ms (0%)

Memory
3.5MiB live, 3.5MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
0.0018900373297351366
0.007120298201771899
Compiler

Compiled 344 to 273 computations (20.6% saved)

bsearch1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
+inf
0.0ms
0.9999966272722692
0.9999999999998741
0.0ms
1.7455162803551408e-6
0.0014498134730074454
0.0ms
-0.21299068980304273
-0.06786085540585546
0.0ms
-0.9621140952183671
-0.8649216765998371
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
+inf
0.0ms
0.9999966272722692
0.9999999999998741
0.0ms
1.7455162803551408e-6
0.0014498134730074454
0.0ms
-0.21299068980304273
-0.06786085540585546
0.0ms
-0.9621140952183671
-0.8649216765998371
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999998741
1.0
0.0ms
1.3691965674196327e-6
1.7455162803551408e-6
0.0ms
-0.06786085540585546
5.777477442801753e-305
0.0ms
-0.9621140952183671
-0.8649216765998371
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999998741
1.0
0.0ms
1.3691965674196327e-6
1.7455162803551408e-6
0.0ms
-0.06786085540585546
5.777477442801753e-305
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999998741
1.0
0.0ms
1.3691965674196327e-6
1.7455162803551408e-6
0.0ms
-0.06786085540585546
5.777477442801753e-305
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999998741
1.0
0.0ms
1.3691965674196327e-6
1.7455162803551408e-6
0.0ms
-0.06786085540585546
5.777477442801753e-305
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.002067476645125004
0.010224877168668272
0.0ms
-0.40319904813161067
-0.3842428563189855
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.0MiB live, 2.0MiB allocated
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.284891708540566
0.2852604626848335
0.0ms
4.656785935183528e-221
4.169029480153179e-220
0.0ms
-1.0
-0.9621140952183671
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
2.635319282473472e-85
5.240001371933364e-85
0.0ms
-0.007988478991256251
3.4879043234463326e-304
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
2.635319282473472e-85
5.240001371933364e-85
0.0ms
-0.007988478991256251
3.4879043234463326e-304
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch2.0ms (0%)

Memory
-45.8MiB live, 0.9MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
2.635319282473472e-85
5.240001371933364e-85
1.0ms
-0.007988478991256251
3.4879043234463326e-304
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
5.223658123632289e-25
2.88189579100648e-18
0.0ms
6.944907720576496e-170
2.7457614377863536e-169
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.002067476645125004
0.010224877168668272
0.0ms
4.656785935183528e-221
4.169029480153179e-220
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.002067476645125004
0.010224877168668272
0.0ms
4.656785935183528e-221
4.169029480153179e-220
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.002067476645125004
0.010224877168668272
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.002067476645125004
0.010224877168668272
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.9743591319371022e-13
3.5379432297835e-9
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch13.0ms (0.1%)

Memory
18.6MiB live, 18.6MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
8.0827349451598e-55
3.55034471989648e-51
Samples
7.0ms128×0valid
Compiler

Compiled 451 to 355 computations (21.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-sin: 3.0ms (73.7% of total)
ival-mult: 1.0ms (24.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.58259336271825e-309
1.5020455350486066e-306
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch8.0ms (0.1%)

Memory
12.1MiB live, 12.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
8.0ms
3.215418756296965e-37
1.275015429307537e-36
Samples
4.0ms80×0valid
Compiler

Compiled 334 to 254 computations (24% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sin: 2.0ms (79.5% of total)
ival-mult: 1.0ms (39.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

simplify80.0ms (0.6%)

Memory
-7.2MiB live, 85.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02802736
13722736
26422736
315102736
436262736
578412736
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8106479329266893/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64)))))) (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 4722366482869645/2361183241434822606848 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 9007181240342483/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 -8106479329266893/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64)))))) (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 4722366482869645/2361183241434822606848 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 9007181240342483/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 -8106479329266893/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64)))))) (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 1770887431076117/1180591620717411303424 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) (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 4503599627369929/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (*.f64 (sin.f64 ky) th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1770887431076117/1180591620717411303424 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) (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 4503599627369929/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1770887431076117/1180591620717411303424 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) (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 4503599627369929/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/72057594037927936 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64)))))) (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 1770887431076117/1180591620717411303424 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) (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 4503599627369929/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64)))))) #s(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 -3602879701896397/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/288230376151711744 binary64)) (*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)) #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 -1 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5134103575202365/18014398509481984 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))))) (sin.f64 th)) (if (<=.f64 (sin.f64 kx) #s(literal 546812681195753/1093625362391505962186251113558810682676584715446606218212885303204976499599687961611756588511526912 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/1152921504606846976 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)))) (if (<=.f64 (sin.f64 kx) #s(literal 546812681195753/1093625362391505962186251113558810682676584715446606218212885303204976499599687961611756588511526912 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/1152921504606846976 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)))) (if (<=.f64 (sin.f64 kx) #s(literal 546812681195753/1093625362391505962186251113558810682676584715446606218212885303204976499599687961611756588511526912 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sin.f64 kx))))))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 6798566308054619/67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 5444517870735015/5444517870735015415413993718908291383296 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) 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 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) 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 1152921504606847/288230376151711744 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 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) 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 1152921504606847/288230376151711744 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 1152921504606847/288230376151711744 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 1152921504606847/288230376151711744 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(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 3961408125713217/19807040628566084398385987584 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky 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 8896782400159711/6739986666787659948666753771754907668409286105635143120275902562304 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (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) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))))
(if (<=.f64 (/.f64 (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 7482888383134223/5986310706507378352962293074805895248510699696029696 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky)))))
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(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 -8106479329266893/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64)))))) (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 4722366482869645/2361183241434822606848 binary64)) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 9007181240342483/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))))
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(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 6798566308054619/67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 5444517870735015/5444517870735015415413993718908291383296 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky))))))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 6798566308054619/67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282123181048810402666930332036061200384 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th)) (if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 5444517870735015/5444517870735015415413993718908291383296 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2))) (sqrt.f64 #s(approx (- 1/2 (* (cos (* -2 kx)) 1/2)) (*.f64 kx kx))))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (pow.f64 #s(approx (- (+ (* (sin ky) (sin ky)) 1/2) (* (cos (* -2 kx)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) (fma.f64 ky ky #s(literal 1/2 binary64)))) #s(literal -1 binary64))) #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) 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 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) 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 1152921504606847/288230376151711744 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 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) 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 1152921504606847/288230376151711744 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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) 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 1152921504606847/288230376151711744 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 5087291284850963/101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (*.f64 (sin.f64 th) 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 1152921504606847/288230376151711744 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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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 1152921504606847/288230376151711744 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 1152921504606847/288230376151711744 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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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 1152921504606847/288230376151711744 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(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 1152921504606847/288230376151711744 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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 3961408125713217/19807040628566084398385987584 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky 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 3961408125713217/19807040628566084398385987584 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (- 1/2 (* (cos (* 2 kx)) 1/2)) (pow (sin ky) 2)))) #s(approx (* (sqrt (/ 1 (+ (* -1/2 (cos (* 2 kx))) 1/2))) ky) (/.f64 ky kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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 8896782400159711/6739986666787659948666753771754907668409286105635143120275902562304 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (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 8896782400159711/6739986666787659948666753771754907668409286105635143120275902562304 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))))
(if (<=.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 1012011266536553/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))))
(if (<=.f64 (/.f64 (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 7482888383134223/5986310706507378352962293074805895248510699696029696 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))))
(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 7482888383134223/5986310706507378352962293074805895248510699696029696 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 #s(literal -1/6 binary64) th) th)) th)))

soundness2.8s (21.9%)

Memory
-42.2MiB live, 1 493.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08245619
131445343
087534907
07334976
127294669
082254319
03171402
111341336
252361308
084061228
053308
085260
1308207
22176204
08957204
045235
078171
1261171
21968171
08146171
069471
0106430
1378345
22713341
010805331
06393996
123573632
091003466
01349
02249
15949
231949
3312949
0893734
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×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 5 590 to 2 403 computations (57% saved)

preprocess252.0ms (2%)

Memory
-16.6MiB live, 412.7MiB allocated
Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 5 770 to 702 computations (87.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...