Toniolo and Linder, Equation (3b), real

Time bar (total: 11.7s)

start0.0ms (0%)

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

analyze453.0ms (3.9%)

Memory
-137.8MiB live, 444.6MiB allocated; 703ms collecting garbage
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 (15.3%)

Memory
82.0MiB live, 2 380.2MiB allocated; 384ms collecting garbage
Samples
1.4s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.2s
ival-sin: 720.0ms (59.4% of total)
ival-pow2: 216.0ms (17.8% of total)
ival-div: 101.0ms (8.3% of total)
ival-sqrt: 66.0ms (5.4% of total)
ival-mult: 57.0ms (4.7% of total)
ival-add: 41.0ms (3.4% of total)
ival-true: 6.0ms (0.5% of total)
adjust: 3.0ms (0.2% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain271.0ms (2.3%)

Memory
0.6MiB live, 187.9MiB allocated; 16ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
110-0-(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-rescue110
↳(pow.f64 (sin.f64 kx) #s(literal 2 binary64))underflow54
↳(pow.f64 (sin.f64 ky) #s(literal 2 binary64))underflow57
↳(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))underflow11
Confusion
Predicted +Predicted -
+110
-0245
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1100
-00245
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0245
111
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
112.0ms512×0valid
Compiler

Compiled 152 to 43 computations (71.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-sin: 48.0ms (51.7% of total)
ival-sqrt: 25.0ms (26.9% of total)
ival-pow2: 10.0ms (10.8% of total)
ival-div: 3.0ms (3.2% of total)
ival-mult: 3.0ms (3.2% of total)
ival-add: 2.0ms (2.2% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess166.0ms (1.4%)

Memory
28.3MiB live, 118.9MiB allocated; 7ms collecting garbage
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)

eval12.0ms (0.1%)

Memory
-50.6MiB live, 0.1MiB allocated; 7ms collecting garbage
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune11.0ms (0.1%)

Memory
7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶95.5%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify152.0ms (1.3%)

Memory
11.4MiB live, 100.4MiB allocated; 7ms collecting garbage
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

localize74.0ms (0.6%)

Memory
10.1MiB live, 55.2MiB allocated; 5ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.17578125
(*.f64 (/.f64 (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))
accuracy0.26466752930532605
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy0.3203125
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy2.6879653026334682
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
Samples
65.0ms256×0valid
Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 56.0ms
ival-pow2: 33.0ms (59.2% of total)
ival-sin: 16.0ms (28.7% of total)
ival-div: 2.0ms (3.6% of total)
ival-mult: 2.0ms (3.6% of total)
ival-sqrt: 2.0ms (3.6% of total)
ival-add: 1.0ms (1.8% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series29.0ms (0.3%)

Memory
20.8MiB live, 20.8MiB allocated; 0ms collecting garbage
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
6.0ms
ky
@0
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
5.0ms
th
@-inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
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
ky
@inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))

simplify234.0ms (2%)

Memory
-32.8MiB live, 162.4MiB allocated; 35ms collecting garbage
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)

rewrite346.0ms (3%)

Memory
14.5MiB live, 295.2MiB allocated; 66ms collecting garbage
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))))

eval76.0ms (0.6%)

Memory
22.7MiB live, 166.0MiB allocated; 37ms collecting garbage
Compiler

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

prune27.0ms (0.2%)

Memory
-26.4MiB live, 65.6MiB allocated; 12ms collecting garbage
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New46419483
Fresh000
Picked011
Done000
Total46420484
Accuracy
100.0%
Counts
484 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶95.9%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
59.7%
(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 ky))) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
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)))))
99.6%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
70.3%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 2 binary64)) (sin.f64 kx))) (sin.f64 th))
▶99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
94.5%
(*.f64 (/.f64 (sin.f64 ky) (*.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)))) (sin.f64 th))
✓95.5%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
42.2%
(*.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))
94.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
86.4%
(*.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))
▶48.0%
(*.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))
28.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
31.6%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
70.1%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
18.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
28.7%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
47.8%
#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)))))))
▶93.4%
#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))))
▶24.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Compiler

Compiled 846 to 631 computations (25.4% saved)

simplify147.0ms (1.3%)

Memory
-3.3MiB live, 163.3MiB allocated; 76ms collecting garbage
Localize:

Found 18 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
035277
057267
190267
2170267
3303267
4572267
51335267
63163267
77083267
08161267
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 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 th)
th
(/.f64 (*.f64 (sin.f64 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)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (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)))
(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 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
(*.f64 (sin.f64 th) (sin.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 #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 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))))
(/.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)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 th)
th
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 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)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (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)))
(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 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th

localize104.0ms (0.9%)

Memory
-0.2MiB live, 190.8MiB allocated; 13ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.21875
(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy0.3203125
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy2.66002034162466
(*.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)))
accuracy2.6960235318306616
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy0.0
(sin.f64 kx)
accuracy0.05078125
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.21875
(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy2.669454081856218
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy0.17578125
(*.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))
accuracy0.3203125
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy2.6879653026334682
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy33.96015971223007
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
accuracy0.0
(sin.f64 th)
accuracy48.58834849455259
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy0.0
(sin.f64 kx)
accuracy0.05078125
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.16796875
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy0.17578125
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Samples
84.0ms256×0valid
Compiler

Compiled 276 to 27 computations (90.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-mult: 21.0ms (32.3% of total)
ival-sin: 21.0ms (32.3% of total)
ival-div: 8.0ms (12.3% of total)
ival-pow2: 5.0ms (7.7% of total)
ival-hypot: 4.0ms (6.1% of total)
ival-sqrt: 3.0ms (4.6% of total)
ival-add: 2.0ms (3.1% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series20.0ms (0.2%)

Memory
-6.3MiB live, 40.6MiB allocated; 2ms collecting garbage
Counts
18 → 80
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (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)))
(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 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(sin.f64 kx)
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
Outputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(/ 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)))
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))))
(* (* (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)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(pow (sin kx) 2)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin 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))
(* 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))))))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(/ 1 (pow (sin kx) 2))
(+ (* -1 (/ (pow ky 2) (pow (sin kx) 4))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6)))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6))))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(* (sin ky) (sin th))
(pow (sin ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* th (sin ky))
(* 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))))))))
Calls

9 calls:

TimeVariablePointExpression
4.0ms
ky
@inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
2.0ms
kx
@inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
2.0ms
ky
@-inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
2.0ms
ky
@0
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
2.0ms
kx
@-inf
((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))

simplify178.0ms (1.5%)

Memory
17.7MiB live, 203.8MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04482190
116192098
275092072
082991959
Stop Event
1×iter limit
1×node limit
Counts
80 → 77
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))))))
(/ 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)))
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))))
(* (* (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)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(pow (sin kx) 2)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin 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))
(* 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))))))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(/ 1 (pow (sin kx) 2))
(+ (* -1 (/ (pow ky 2) (pow (sin kx) 4))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6)))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6))))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(* (sin ky) (sin th))
(pow (sin ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* th (sin ky))
(* 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))))))))
Outputs
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (*.f64 (*.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)))) (*.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (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 #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 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))
(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 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 ky)) (*.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 ky))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 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)))
(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)))) (sin.f64 ky)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1 binary64) (sin.f64 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)))
(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))))) (sin.f64 ky)) (*.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)))) (sin.f64 ky)))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/ 1 (pow (sin ky) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ (* (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)))
(fma.f64 (-.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 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)))) (*.f64 kx kx)) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ (* (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)))
(fma.f64 (-.f64 (*.f64 (fma.f64 (neg.f64 (+.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))))) (*.f64 kx kx) (+.f64 (/.f64 #s(literal 1 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))))) (*.f64 kx kx)) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 kx kx)) #s(literal 1/6 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (-.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)
(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))))
(*.f64 (*.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)) 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 (*.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) #s(literal 1 binary64)) (*.f64 kx kx))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(sin kx)
(sin.f64 kx)
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (sin.f64 th) (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(*.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (sin.f64 th)) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (*.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (sin.f64 th)) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (fma.f64 (*.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (sin.f64 th)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 (fma.f64 #s(literal -1/5040 binary64) (sin.f64 th) (/.f64 (*.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (sin.f64 th)) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (*.f64 ky (*.f64 (neg.f64 ky) ky)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/6 binary64)) (sin.f64 kx)) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (-.f64 (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky)) (/.f64 (+.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))) (+ (* 1/12 (/ 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 (*.f64 (+.f64 (fma.f64 (-.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 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (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))))))) (/.f64 (+.f64 (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/5040 binary64)) (sin.f64 kx))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky)) (/.f64 (+.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
(* 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 (*.f64 ky ky) #s(literal 1/120 binary64)) #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 (*.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 #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 (fma.f64 (/.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)) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx))
(* 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)))))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (*.f64 (sin.f64 th) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 (sin.f64 th) ky))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (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 (sin.f64 th) ky))
(/ 1 (sin kx))
(/.f64 #s(literal 1 binary64) (sin.f64 kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(fma.f64 (*.f64 ky (/.f64 ky (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(fma.f64 (fma.f64 (*.f64 (*.f64 ky ky) #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 kx)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(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 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 ky ky)) (*.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 kx)))) (*.f64 ky ky) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))
(/ 1 (pow (sin kx) 2))
(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(+ (* -1 (/ (pow ky 2) (pow (sin kx) 4))) (/ 1 (pow (sin kx) 2)))
(fma.f64 (*.f64 ky (/.f64 ky (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6)))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(fma.f64 (-.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 ky ky)) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 ky ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6))))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(fma.f64 (-.f64 (*.f64 (fma.f64 (neg.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (*.f64 ky ky) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (*.f64 ky ky)) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 ky ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(*.f64 (*.f64 (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))))
(*.f64 (*.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)) ky) ky)
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.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) #s(literal 1 binary64)) (*.f64 ky ky))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.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))))))))))
(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))))) th) (sin.f64 ky) (*.f64 (pow.f64 th #s(literal 3 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) (*.f64 (*.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))))) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) th) th) #s(literal 1/6 binary64)) th)
(* th (sin ky))
(*.f64 (sin.f64 ky) th)
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) (*.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 (sin.f64 ky) th))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) (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 (sin.f64 ky) th))

rewrite162.0ms (1.4%)

Memory
12.7MiB live, 200.1MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035204
057179
1183179
21188175
08684175
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 381
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (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)))
(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 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(sin.f64 kx)
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
Outputs
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 (/.f64 (-.f64 (-.f64 th ky) (+.f64 th ky)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (-.f64 th ky) (+.f64 th ky)) #s(literal 2 binary64)))) (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 (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 (neg.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)))) (neg.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky)))) (neg.f64 (*.f64 #s(literal 2 binary64) (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 th ky))) (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (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 th) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(-.f64 (/.f64 (cos.f64 (-.f64 th ky)) (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (cos.f64 (+.f64 th ky)) (*.f64 #s(literal 2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(-.f64 (/.f64 (/.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (/.f64 (cos.f64 (+.f64 th ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(/.f64 (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 1/4 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))))
(*.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))))))
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(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
(/.f64 (neg.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)))) (neg.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 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 4 binary64))
(/.f64 (fabs.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (fabs.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))))
(/.f64 (fabs.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))) #s(literal 2 binary64))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (neg.f64 ky) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (+.f64 (neg.f64 ky) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 ky (PI.f64)) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64))))) (sin.f64 (+.f64 (+.f64 ky (PI.f64)) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 ky) (neg.f64 ky))) (cos.f64 (+.f64 (neg.f64 ky) (neg.f64 ky)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (neg.f64 ky) (+.f64 ky (PI.f64)))) (cos.f64 (+.f64 (neg.f64 ky) (+.f64 ky (PI.f64))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 ky (PI.f64)) (neg.f64 ky))) (cos.f64 (+.f64 (+.f64 ky (PI.f64)) (neg.f64 ky)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 ky (PI.f64)) (+.f64 ky (PI.f64)))) (cos.f64 (+.f64 (+.f64 ky (PI.f64)) (+.f64 ky (PI.f64))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (-.f64 (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))
(neg.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 ky))))
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))) (/.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #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 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (neg.f64 ky)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 ky (PI.f64))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(fabs.f64 (-.f64 (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(fabs.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))
(fabs.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 ky))))
(fabs.f64 (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fabs.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (sin.f64 ky))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 ky (/.f64 (PI.f64) #s(literal 2 binary64)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))

eval189.0ms (1.6%)

Memory
-0.5MiB live, 241.1MiB allocated; 38ms collecting garbage
Compiler

Compiled 27 195 to 3 335 computations (87.7% saved)

prune49.0ms (0.4%)

Memory
-28.1MiB live, 112.3MiB allocated; 19ms collecting garbage
Pruning

34 alts after pruning (31 fresh and 3 done)

PrunedKeptTotal
New84723870
Fresh6814
Picked235
Done101
Total85634890
Accuracy
100.0%
Counts
890 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
36.6%
(/.f64 (*.f64 (sin.f64 th) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
28.3%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 kx))) (sqrt.f64 (neg.f64 (sin.f64 kx))))))
81.8%
(/.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)))
29.5%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
▶41.2%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
41.5%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
48.6%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
59.7%
(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 ky))) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶99.6%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
✓99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
81.9%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
▶81.6%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
42.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
86.4%
(*.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))
✓48.0%
(*.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))
43.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
22.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
28.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
31.6%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
47.9%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
18.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
28.7%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
95.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 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))))
88.9%
#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) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
40.3%
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
40.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
40.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
95.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
▶29.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
28.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
✓24.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
11.6%
#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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
▶11.7%
#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)))
49.3%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (*.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))
Compiler

Compiled 1 722 to 1 258 computations (26.9% saved)

simplify111.0ms (0.9%)

Memory
37.7MiB live, 135.9MiB allocated; 12ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 ky)
cost-diff0
(/.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))))
cost-diff0
(*.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))
cost-diff2
(+.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))))
cost-diff0
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th))
cost-diff0
#s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky))
cost-diff0
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff2
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
cost-diff0
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
cost-diff0
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
cost-diff0
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky)))
cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
cost-diff0
(pow.f64 th #s(literal 3 binary64))
cost-diff0
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
cost-diff0
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
cost-diff0
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 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
054388
089375
1155375
2320365
3722365
41767362
53590362
66374362
08134359
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) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(pow.f64 th #s(literal 3 binary64))
th
#s(literal 3 binary64)
#s(literal -1/6 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
#s(literal 1 binary64)
(sin.f64 ky)
ky
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 ky ky)
ky
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(sin.f64 th)
th
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 ky)
(sin.f64 kx)
kx
(*.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 (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 ky)
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)))
(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)))))
(+.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))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
(*.f64 #s(literal 2 binary64) ky)
#s(literal 2 binary64)
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
kx
(sqrt.f64 #s(literal 2 binary64))
(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 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(/.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) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
#s(approx (sin th) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)
(pow.f64 th #s(literal 3 binary64))
th
#s(literal 3 binary64)
#s(literal -1/6 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky)) (sin.f64 th)))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky)) (sin.f64 th))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
#s(literal 1 binary64)
(sin.f64 ky)
ky
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky) (sin.f64 th))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
#s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky))
#s(approx (* (sin th) (sin ky)) (*.f64 (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky) (sin.f64 th)))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(*.f64 (fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky) (sin.f64 th))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 ky ky)
ky
#s(literal -1/6 binary64)
#s(literal 1 binary64)
(sin.f64 th)
th
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
(sin.f64 kx)
kx
(*.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 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sin.f64 th)) (sqrt.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))))
(/.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))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))))
(sin.f64 ky)
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)))
(/.f64 (sqrt.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))
(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 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))
(+.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))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))
(-.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) ky)))
#s(literal 1 binary64)
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
(*.f64 #s(literal 2 binary64) ky)
#s(literal 2 binary64)
(-.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) kx)))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(cos.f64 (*.f64 #s(literal -2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
kx
(sqrt.f64 #s(literal 2 binary64))
(sin.f64 th)
th

localize421.0ms (3.6%)

Memory
-2.6MiB live, 520.5MiB allocated; 61ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.4498825195368841
(/.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)))
accuracy2.6997961521321328
(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)))))
accuracy12.470433848275551
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
accuracy14.095651902132207
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
accuracy0.1171875
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
accuracy2.669454081856218
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy4.789545622196702
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th))
accuracy35.1466550665631
#s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky))
accuracy0.1640625
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
accuracy0.21875
(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy2.66002034162466
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky)))
accuracy48.90519911611841
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
accuracy0.0
(pow.f64 th #s(literal 3 binary64))
accuracy0.05078125
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
accuracy30.635464679139062
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
accuracy48.58834849455259
#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)))
accuracy0.0
(sin.f64 kx)
accuracy0.05078125
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.25390625
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy0.26953125
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
Samples
157.0ms102×2valid
147.0ms77×1valid
48.0ms77×0valid
Compiler

Compiled 353 to 49 computations (86.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 307.0ms
ival-cos: 80.0ms (26.1% of total)
adjust: 46.0ms (15% of total)
ival-div: 41.0ms (13.4% of total)
ival-mult: 36.0ms (11.7% of total)
ival-sin: 24.0ms (7.8% of total)
ival-sub: 19.0ms (6.2% of total)
ival-pow2: 19.0ms (6.2% of total)
ival-sqrt: 11.0ms (3.6% of total)
ival-add: 10.0ms (3.3% of total)
ival-pow: 8.0ms (2.6% of total)
ival-hypot: 7.0ms (2.3% of total)
const: 6.0ms (2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series79.0ms (0.7%)

Memory
-23.3MiB live, 162.6MiB allocated; 31ms collecting garbage
Counts
26 → 146
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))
#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) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(pow.f64 th #s(literal 3 binary64))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th))
(+.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))))
(*.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 (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 ky)
(sin.f64 kx)
(*.f64 (sin.f64 th) (sin.f64 ky))
(-.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 (+.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)))))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(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))))))
(/ 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 (cos (* 2 ky)))
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky)))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -1 (* (* (pow kx 2) (* (sin ky) (* (sin th) (sqrt 2)))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sin ky) (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -1 (* (* (pow kx 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sin ky) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (sqrt (- 1 (cos (* 2 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))))
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(sqrt (- 1 (cos (* 2 ky))))
(+ (sqrt (- 1 (cos (* 2 ky)))) (* (pow kx 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (sqrt (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* -1/2 (* (* (pow kx 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky)))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))
(+ (sqrt (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (* (pow kx 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (- 1 (cos (* 2 ky))))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky)))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(* (* (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)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(sin kx)
(- 1 (cos (* 2 kx)))
(sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* (/ 1 (sqrt 2)) (sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin 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))))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(/ 1 ky)
(/ (+ 1 (* 1/6 (pow ky 2))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* 7/360 (pow ky 2))))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* (pow ky 2) (+ 7/360 (* 31/15120 (pow ky 2))))))) ky)
(* 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 th) (* -1/6 (* (pow ky 2) (sin th))))
(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx)))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(sqrt (- 1 (cos (* 2 kx))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* -1/2 (* (* (pow ky 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (* (pow ky 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(* -1/6 (* (pow ky 3) (sin th)))
(* (pow ky 3) (+ (* -1/6 (sin th)) (/ (sin th) (pow ky 2))))
(* (sin ky) (sin th))
(* -1/6 (* (pow ky 2) (sin th)))
(* (pow ky 2) (+ (* -1/6 (sin th)) (/ (sin th) (pow ky 2))))
(* -1 (* (pow ky 3) (+ (* -1 (/ (sin th) (pow ky 2))) (* 1/6 (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))))
(pow th 3)
(* ky (* th (+ 1 (* -1/6 (pow ky 2)))))
(* th (+ (* -1/6 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))))) (* ky (+ 1 (* -1/6 (pow ky 2))))))
(* th (+ (* ky (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/6 (* ky (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))))))))
(* th (+ (* ky (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/6 (* ky (+ 1 (* -1/6 (pow ky 2))))) (* (pow th 2) (+ (* -1/5040 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))))) (* 1/120 (* ky (+ 1 (* -1/6 (pow ky 2)))))))))))
(* th (sin ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(* th (+ 1 (* -1/6 (pow ky 2))))
(* th (+ 1 (+ (* -1/6 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))) (* -1/6 (pow ky 2)))))
(* th (+ 1 (+ (* -1/6 (pow ky 2)) (* (pow th 2) (+ (* -1/6 (+ 1 (* -1/6 (pow ky 2)))) (* 1/120 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))))))))
(* th (+ 1 (+ (* -1/6 (pow ky 2)) (* (pow th 2) (+ (* -1/6 (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (+ 1 (* -1/6 (pow ky 2)))))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))
(* th (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/120 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))))))))
(* th (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/120 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))))))))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* ky (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))
(* (sin th) (+ 1 (* -1/6 (pow ky 2))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
Calls

9 calls:

TimeVariablePointExpression
14.0ms
kx
@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)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (sin ky)) (* (* (+ (* (* ky ky) -1/6) 1) (sin th)) ky) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* ky ky) -1/6) 1) (sin th)) (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin ky) (sin kx) (* (sin th) (sin ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2)))
12.0ms
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)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (sin ky)) (* (* (+ (* (* ky ky) -1/6) 1) (sin th)) ky) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* ky ky) -1/6) 1) (sin th)) (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin ky) (sin kx) (* (sin th) (sin ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2)))
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)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (sin ky)) (* (* (+ (* (* ky ky) -1/6) 1) (sin th)) ky) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* ky ky) -1/6) 1) (sin th)) (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin ky) (sin kx) (* (sin th) (sin ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2)))
9.0ms
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)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (sin ky)) (* (* (+ (* (* ky ky) -1/6) 1) (sin th)) ky) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* ky ky) -1/6) 1) (sin th)) (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin ky) (sin kx) (* (sin th) (sin ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2)))
8.0ms
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)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (sin ky)) (* (* (+ (* (* ky ky) -1/6) 1) (sin th)) ky) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (* (+ (* (* ky ky) -1/6) 1) (sin th)) (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin ky) (sin kx) (* (sin th) (sin ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* 2 ky))) (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2)))

simplify236.0ms (2%)

Memory
34.9MiB live, 317.1MiB allocated; 43ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08275514
131575185
081414948
Stop Event
1×iter limit
1×node limit
Counts
146 → 143
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))))))
(/ 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 (cos (* 2 ky)))
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky)))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -1 (* (* (pow kx 2) (* (sin ky) (* (sin th) (sqrt 2)))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sin ky) (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -1 (* (* (pow kx 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sin ky) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (sqrt (- 1 (cos (* 2 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))))
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(sqrt (- 1 (cos (* 2 ky))))
(+ (sqrt (- 1 (cos (* 2 ky)))) (* (pow kx 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (sqrt (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* -1/2 (* (* (pow kx 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky)))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))
(+ (sqrt (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (* (pow kx 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (- 1 (cos (* 2 ky))))))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))) (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 ky)))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 ky))))) (- 1 (cos (* 2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(* (* (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)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(sin kx)
(- 1 (cos (* 2 kx)))
(sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* (/ 1 (sqrt 2)) (sqrt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin 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))))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(/ 1 ky)
(/ (+ 1 (* 1/6 (pow ky 2))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* 7/360 (pow ky 2))))) ky)
(/ (+ 1 (* (pow ky 2) (+ 1/6 (* (pow ky 2) (+ 7/360 (* 31/15120 (pow ky 2))))))) ky)
(* 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 th) (* -1/6 (* (pow ky 2) (sin th))))
(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx)))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(sqrt (- 1 (cos (* 2 kx))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* -1/2 (* (* (pow ky 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (* (pow ky 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(* -1/6 (* (pow ky 3) (sin th)))
(* (pow ky 3) (+ (* -1/6 (sin th)) (/ (sin th) (pow ky 2))))
(* (sin ky) (sin th))
(* -1/6 (* (pow ky 2) (sin th)))
(* (pow ky 2) (+ (* -1/6 (sin th)) (/ (sin th) (pow ky 2))))
(* -1 (* (pow ky 3) (+ (* -1 (/ (sin th) (pow ky 2))) (* 1/6 (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))))
(pow th 3)
(* ky (* th (+ 1 (* -1/6 (pow ky 2)))))
(* th (+ (* -1/6 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))))) (* ky (+ 1 (* -1/6 (pow ky 2))))))
(* th (+ (* ky (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/6 (* ky (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))))))))
(* th (+ (* ky (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/6 (* ky (+ 1 (* -1/6 (pow ky 2))))) (* (pow th 2) (+ (* -1/5040 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))))) (* 1/120 (* ky (+ 1 (* -1/6 (pow ky 2)))))))))))
(* th (sin ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(* th (+ 1 (* -1/6 (pow ky 2))))
(* th (+ 1 (+ (* -1/6 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))) (* -1/6 (pow ky 2)))))
(* th (+ 1 (+ (* -1/6 (pow ky 2)) (* (pow th 2) (+ (* -1/6 (+ 1 (* -1/6 (pow ky 2)))) (* 1/120 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))))))))
(* th (+ 1 (+ (* -1/6 (pow ky 2)) (* (pow th 2) (+ (* -1/6 (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (+ 1 (* -1/6 (pow ky 2)))))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))
(* th (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/120 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))))))))
(* th (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/120 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))))))))))
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* ky (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))
(* (sin th) (+ 1 (* -1/6 (pow ky 2))))
(* -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))))))))))))
(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))
(/ (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 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)) (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 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)) (sin.f64 ky)) (*.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)) (sin.f64 ky)))) (*.f64 kx kx) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (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 (*.f64 kx kx) (sin.f64 ky)) #s(literal 1/2 binary64) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 kx kx)) #s(literal 1/2 binary64)) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
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(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
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kx
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(* 2 (pow kx 2))
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(sqrt (- 1 (cos (* 2 ky))))
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(* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))
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(/ (* ky (sin th)) (sin kx))
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(/ (sin th) (sin kx))
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(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
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(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx)))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* (sin th) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (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))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* 2 (pow ky 2))
(*.f64 (*.f64 ky ky) #s(literal 2 binary64))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 4/45 binary64)) #s(literal 2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) (*.f64 ky ky)) #s(literal 2/3 binary64)) (*.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky))
(sqrt (- 1 (cos (* 2 kx))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* -1/2 (* (* (pow ky 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2/3 binary64)) (*.f64 ky ky)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) (*.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))
(+ (sqrt (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (* (pow ky 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))))))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 #s(literal 4/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 ky ky)) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal -1/2 binary64) #s(literal -1/3 binary64)))) (*.f64 ky ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) (*.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))
(* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 ky ky) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 2/3 (/ 1 (- 1 (cos (* 2 kx)))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2/3 binary64)) (*.f64 ky ky)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 ky ky) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (/ 1 (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 4/45 (* -1 (/ (+ 2/3 (/ 1 (- 1 (cos (* 2 kx))))) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 ky ky) (/.f64 (+.f64 #s(literal 4/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 ky ky) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))))
(* -1/6 (* (pow ky 3) (sin th)))
(*.f64 (*.f64 #s(literal -1/6 binary64) (pow.f64 ky #s(literal 3 binary64))) (sin.f64 th))
(* (pow ky 3) (+ (* -1/6 (sin th)) (/ (sin th) (pow ky 2))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 th) (/.f64 (sin.f64 th) (*.f64 ky ky))) (pow.f64 ky #s(literal 3 binary64)))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* -1/6 (* (pow ky 2) (sin th)))
(*.f64 (*.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) (sin.f64 th))
(* (pow ky 2) (+ (* -1/6 (sin th)) (/ (sin th) (pow ky 2))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (sin.f64 th) (/.f64 (sin.f64 th) (*.f64 ky ky))) (*.f64 ky ky))
(* -1 (* (pow ky 3) (+ (* -1 (/ (sin th) (pow ky 2))) (* 1/6 (sin th)))))
(*.f64 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (fma.f64 #s(literal 1/6 binary64) (sin.f64 th) (/.f64 (neg.f64 (sin.f64 th)) (*.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 (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)
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(* ky (* th (+ 1 (* -1/6 (pow ky 2)))))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)
(* th (+ (* -1/6 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))))) (* ky (+ 1 (* -1/6 (pow ky 2))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) ky) (*.f64 (*.f64 th th) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)
(* th (+ (* ky (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/6 (* ky (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) ky) (*.f64 (*.f64 th th) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky) #s(literal -1/6 binary64))) (*.f64 th th) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)) th)
(* th (+ (* ky (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/6 (* ky (+ 1 (* -1/6 (pow ky 2))))) (* (pow th 2) (+ (* -1/5040 (* ky (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))))) (* 1/120 (* ky (+ 1 (* -1/6 (pow ky 2)))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) ky) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 #s(literal -1/5040 binary64) ky) (*.f64 (*.f64 th th) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky) #s(literal 1/120 binary64))) (*.f64 th th))) (*.f64 th th) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)
(* th (+ 1 (* -1/6 (pow ky 2))))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (+ (* -1/6 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))) (* -1/6 (pow ky 2)))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (fma.f64 (*.f64 th th) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 ky ky)) #s(literal 1 binary64)) th)
(* th (+ 1 (+ (* -1/6 (pow ky 2)) (* (pow th 2) (+ (* -1/6 (+ 1 (* -1/6 (pow ky 2)))) (* 1/120 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))))))))
(*.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 th th) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))) th)
(* th (+ 1 (+ (* -1/6 (pow ky 2)) (* (pow th 2) (+ (* -1/6 (+ 1 (* -1/6 (pow ky 2)))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (+ 1 (* -1/6 (pow ky 2)))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 th th) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) #s(literal -1/6 binary64))) (*.f64 th th) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))) th)
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))
(* th (+ (* -1/6 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (*.f64 th th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)))) th)
(* th (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/120 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (*.f64 th th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)))) th)
(* th (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))) (* 1/120 (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (*.f64 th th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 th th) (*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)))) th)
(* -1/6 (pow th 3))
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(* ky (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))
(*.f64 (*.f64 (sin.f64 th) ky) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(* (sin th) (+ 1 (* -1/6 (pow ky 2))))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 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)))

rewrite194.0ms (1.7%)

Memory
-0.7MiB live, 274.6MiB allocated; 46ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054325
089272
1309272
22277261
09847261
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
26 → 474
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))
#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) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(pow.f64 th #s(literal 3 binary64))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th))
(+.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))))
(*.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 (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 ky)
(sin.f64 kx)
(*.f64 (sin.f64 th) (sin.f64 ky))
(-.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 (+.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)))))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (neg.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))))))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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 (/.f64 (sin.f64 ky) (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)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))
(*.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 th)) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (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))) (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 (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))
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(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) #s(literal 2 binary64)))) (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))))))
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(/.f64 (hypot.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (-.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)))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64)))))
(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)))))
(exp.f64 (*.f64 (log.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))))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.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))))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.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))))) #s(literal 1/2 binary64))))
(*.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 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))) #s(literal 2 binary64))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 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 (neg.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 (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 (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 (neg.f64 (neg.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))))))) (neg.f64 (neg.f64 (sqrt.f64 #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 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 2 binary64))))
(/.f64 (hypot.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) #s(literal 3/2 binary64))) (sqrt.f64 (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))) (-.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)))) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 (neg.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)))))) (neg.f64 (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)))
(neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(hypot.f64 (neg.f64 (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 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 (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 (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))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (neg.f64 (sin.f64 kx)))))
(hypot.f64 (sin.f64 ky) (pow.f64 (neg.f64 (neg.f64 (sin.f64 kx))) #s(literal 1 binary64)))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(exp.f64 (-.f64 (*.f64 (log.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))))) #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 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)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))

eval167.0ms (1.4%)

Memory
12.1MiB live, 378.0MiB allocated; 103ms collecting garbage
Compiler

Compiled 29 151 to 3 434 computations (88.2% saved)

prune170.0ms (1.4%)

Memory
-0.4MiB live, 261.3MiB allocated; 135ms collecting garbage
Pruning

56 alts after pruning (53 fresh and 3 done)

PrunedKeptTotal
New72942771
Fresh151126
Picked325
Done213
Total74956805
Accuracy
100.0%
Counts
805 → 56
Alt Table
Click to see full alt table
StatusAccuracyProgram
81.8%
(/.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)))
13.3%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 kx))) (sqrt.f64 (neg.f64 (sin.f64 kx))))))
47.2%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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)))
14.2%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
48.6%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
19.4%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
81.6%
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (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)))))) (sin.f64 th))
81.5%
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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)))
70.9%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))
✓99.6%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
44.9%
(*.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)))
▶51.8%
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
46.4%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
24.1%
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
42.5%
(*.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)))
29.4%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
32.8%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
81.6%
(*.f64 (/.f64 (sin.f64 ky) (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)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))
▶43.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
22.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
31.6%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
52.0%
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
28.0%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
81.6%
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th))
81.6%
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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)))
31.6%
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
33.2%
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
27.4%
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
18.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
28.7%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
25.5%
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
49.3%
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
42.6%
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
32.9%
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
27.3%
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
24.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
40.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
▶95.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
17.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
✓29.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
45.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
14.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
▶17.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
28.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
15.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
16.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
16.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
✓24.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
11.6%
#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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th th) th) #s(literal -1/6 binary64) th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
▶11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
9.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
4.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
Compiler

Compiled 3 491 to 2 508 computations (28.2% saved)

simplify145.0ms (1.2%)

Memory
-2.3MiB live, 188.5MiB allocated; 21ms collecting garbage
Localize:

Found 20 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
060509
0101485
1191484
2449476
31068467
42548467
08050449
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
(sin.f64 ky)
ky
#s(literal -1 binary64)
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)
(*.f64 #s(literal -1/6 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)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
#s(literal 1 binary64)
(sin.f64 ky)
ky
(*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))
#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)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
(*.f64 #s(literal 2 binary64) ky)
#s(literal 2 binary64)
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(/.f64 (sin.f64 th) (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))))
(sin.f64 th)
th
(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)))
(sin.f64 ky)
ky
#s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 kx kx)
kx
#s(literal 1 binary64)
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)))
(*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64))
(*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(neg.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
(sin.f64 ky)
ky
#s(literal -1 binary64)
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th 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) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th))
#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
#s(literal -1/6 binary64)
(*.f64 th th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)))
(*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
#s(literal 1 binary64)
(sin.f64 ky)
ky
(*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))
(*.f64 #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) (sin.f64 ky))
#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))
(*.f64 th th)
th
#s(literal -1/6 binary64)
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))
(sqrt.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
(+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
(*.f64 #s(literal 2 binary64) ky)
#s(literal 2 binary64)
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (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))))
(/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)) (sin.f64 ky)))
(sin.f64 th)
th
(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)))
(hypot.f64 #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)) (sin.f64 ky))
(sin.f64 ky)
ky
#s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))
#s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (*.f64 kx kx) #s(literal -1/6 binary64) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 kx kx)
kx
#s(literal 1 binary64)

localize407.0ms (3.5%)

Memory
-15.1MiB live, 554.7MiB allocated; 71ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.11947250976844202
(fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64))
accuracy0.25390625
(/.f64 (sin.f64 th) (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))))
accuracy0.26953125
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
accuracy34.430888556545185
#s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))
accuracy0.24837600585508707
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
accuracy2.6879653026334682
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))
accuracy12.460901133586804
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
accuracy33.96015971223007
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
accuracy0.21875
(*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))
accuracy2.66002034162466
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)))
accuracy30.635464679139062
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy48.90519911611841
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
accuracy0.05859375
(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)
accuracy0.203125
(*.f64 #s(literal -1/6 binary64) (*.f64 th th))
accuracy30.635464679139062
#s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th))
accuracy48.58834849455259
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
accuracy0.21875
(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy0.9668116513497179
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
accuracy1.1007609314034161
(log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
accuracy2.66002034162466
(*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky)))
Samples
98.0ms146×0valid
93.0ms52×2valid
81.0ms58×1valid
Compiler

Compiled 408 to 53 computations (87% saved)

Precisions
Click to see histograms. Total time spent on operations: 234.0ms
ival-sin: 46.0ms (19.7% of total)
ival-cos: 42.0ms (18% of total)
ival-mult: 38.0ms (16.3% of total)
ival-hypot: 31.0ms (13.3% of total)
adjust: 18.0ms (7.7% of total)
ival-add: 13.0ms (5.6% of total)
ival-div: 11.0ms (4.7% of total)
ival-pow2: 10.0ms (4.3% of total)
ival-sqrt: 8.0ms (3.4% of total)
const: 5.0ms (2.1% of total)
ival-exp: 4.0ms (1.7% of total)
ival-log: 4.0ms (1.7% of total)
ival-sub: 2.0ms (0.9% of total)
exact: 1.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series238.0ms (2%)

Memory
45.0MiB live, 269.1MiB allocated; 63ms collecting garbage
Counts
29 → 127
Calls
Call 1
Inputs
(*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th))
(*.f64 #s(literal -1/6 binary64) (*.f64 th 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)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))))
(sin.f64 ky)
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(/.f64 (sin.f64 th) (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))))
(sin.f64 th)
(log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (sin.f64 th) (sin.f64 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 th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
#s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))
(fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 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 (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 (log (sin ky)))
(+ (* -1 (log (sin ky))) (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ (* -1 (log (sin ky))) (* (pow kx 2) (- (* -1/24 (* (pow kx 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4)))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ (* -1 (log (sin ky))) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4))))) (* -1/720 (* (pow kx 2) (+ (* 30 (/ 1 (pow (sin ky) 6))) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 4))) (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2)))) (pow (sin ky) 2))))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))))
(* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 4))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(/ (sin th) (sin ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(log (sin ky))
(+ (log (sin ky)) (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ (log (sin ky)) (* (pow kx 2) (+ (* 1/24 (* (pow kx 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4)))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ (log (sin ky)) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/720 (* (pow kx 2) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 4))) (+ (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 30 (/ 1 (pow (sin ky) 6))))))) (* 1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4))))))) (* 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 (- 1/2 (* 1/2 (cos (* 2 ky)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
(* 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))))
1
(+ 1 (* -1/6 (pow kx 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* -1 (log (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
(* -1/6 (pow kx 3))
(* (pow kx 3) (- (/ 1 (pow kx 2)) 1/6))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(log (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))
(sin kx)
(* -1/6 (pow kx 2))
(* (pow kx 2) (- (/ 1 (pow kx 2)) 1/6))
(* -1 (* (pow kx 3) (- 1/6 (/ 1 (pow kx 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(* -1 (log (sin kx)))
(+ (* -1 (log (sin kx))) (* -1/2 (/ (pow ky 2) (pow (sin kx) 2))))
(+ (* -1 (log (sin kx))) (* (pow ky 2) (- (* -1/24 (* (pow ky 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4)))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(+ (* -1 (log (sin kx))) (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4))))) (* -1/720 (* (pow ky 2) (+ (* 30 (/ 1 (pow (sin kx) 6))) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 4))) (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (pow (sin kx) 2))))))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(/ 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 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)))
(log (sin kx))
(+ (log (sin kx)) (* 1/2 (/ (pow ky 2) (pow (sin kx) 2))))
(+ (log (sin kx)) (* (pow ky 2) (+ (* 1/24 (* (pow ky 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4)))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(+ (log (sin kx)) (* (pow ky 2) (+ (* (pow ky 2) (+ (* 1/720 (* (pow ky 2) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 4))) (+ (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 30 (/ 1 (pow (sin kx) 6))))))) (* 1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4))))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(+ (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 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 2/3 (pow ky 2)) 2)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/3 (* -4/45 (pow ky 2)))) 2)))
(- 1/2 (* 1/2 (cos (* 2 ky))))
(sin ky)
(* (sin ky) (sin th))
(cos (* 2 ky))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* -1/6 (pow th 2))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))))))))))
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(* 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 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
Calls

9 calls:

TimeVariablePointExpression
70.0ms
kx
@inf
((* (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (sin th) (sin ky))) (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (+ (* (* -1/6 (* th th)) th) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (- 1/2 (* (cos (* 2 ky)) 1/2)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin ky) (* (+ (* -1/6 (* kx kx)) 1) kx) (* (/ (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) (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (* (sin th) (sin ky)) (pow (sin kx) 2) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (sin kx) (+ (* -1/6 (* kx kx)) 1))
69.0ms
ky
@inf
((* (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (sin th) (sin ky))) (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (+ (* (* -1/6 (* th th)) th) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (- 1/2 (* (cos (* 2 ky)) 1/2)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin ky) (* (+ (* -1/6 (* kx kx)) 1) kx) (* (/ (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) (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (* (sin th) (sin ky)) (pow (sin kx) 2) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (sin kx) (+ (* -1/6 (* kx kx)) 1))
38.0ms
ky
@-inf
((* (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (sin th) (sin ky))) (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (+ (* (* -1/6 (* th th)) th) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (- 1/2 (* (cos (* 2 ky)) 1/2)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin ky) (* (+ (* -1/6 (* kx kx)) 1) kx) (* (/ (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) (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (* (sin th) (sin ky)) (pow (sin kx) 2) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (sin kx) (+ (* -1/6 (* kx kx)) 1))
32.0ms
kx
@-inf
((* (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (sin th) (sin ky))) (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (+ (* (* -1/6 (* th th)) th) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (- 1/2 (* (cos (* 2 ky)) 1/2)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin ky) (* (+ (* -1/6 (* kx kx)) 1) kx) (* (/ (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) (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (* (sin th) (sin ky)) (pow (sin kx) 2) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (sin kx) (+ (* -1/6 (* kx kx)) 1))
9.0ms
kx
@0
((* (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (sin th) (sin ky))) (exp (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1)) (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (+ (* (* -1/6 (* th th)) th) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* (+ (* (* th th) -1/6) 1) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin th) (sin ky))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (- 1/2 (* (cos (* 2 ky)) 1/2)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (sin ky) (* (+ (* -1/6 (* kx kx)) 1) kx) (* (/ (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) (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (* (sin th) (sin ky)) (pow (sin kx) 2) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (sin kx) (+ (* -1/6 (* kx kx)) 1))

simplify317.0ms (2.7%)

Memory
4.7MiB live, 232.8MiB allocated; 40ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06934135
125053910
081663660
Stop Event
1×iter limit
1×node limit
Counts
127 → 124
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 (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 (log (sin ky)))
(+ (* -1 (log (sin ky))) (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ (* -1 (log (sin ky))) (* (pow kx 2) (- (* -1/24 (* (pow kx 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4)))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ (* -1 (log (sin ky))) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4))))) (* -1/720 (* (pow kx 2) (+ (* 30 (/ 1 (pow (sin ky) 6))) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 4))) (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2)))) (pow (sin ky) 2))))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 4)))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))))
(* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3)))) (- 1/2 (* 1/2 (cos (* 2 ky)))))) (+ (* 2/45 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (+ (* 2/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))) (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 4))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(/ (sin th) (sin ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(log (sin ky))
(+ (log (sin ky)) (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ (log (sin ky)) (* (pow kx 2) (+ (* 1/24 (* (pow kx 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4)))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ (log (sin ky)) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/720 (* (pow kx 2) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 4))) (+ (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 30 (/ 1 (pow (sin ky) 6))))))) (* 1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4))))))) (* 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 (- 1/2 (* 1/2 (cos (* 2 ky)))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (- 1/2 (* 1/2 (cos (* 2 ky)))))))) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
(* 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))))
1
(+ 1 (* -1/6 (pow kx 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* -1 (log (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
(* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
(* -1/6 (pow kx 3))
(* (pow kx 3) (- (/ 1 (pow kx 2)) 1/6))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(log (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))
(sin kx)
(* -1/6 (pow kx 2))
(* (pow kx 2) (- (/ 1 (pow kx 2)) 1/6))
(* -1 (* (pow kx 3) (- 1/6 (/ 1 (pow kx 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 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)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(* -1 (log (sin kx)))
(+ (* -1 (log (sin kx))) (* -1/2 (/ (pow ky 2) (pow (sin kx) 2))))
(+ (* -1 (log (sin kx))) (* (pow ky 2) (- (* -1/24 (* (pow ky 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4)))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(+ (* -1 (log (sin kx))) (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4))))) (* -1/720 (* (pow ky 2) (+ (* 30 (/ 1 (pow (sin kx) 6))) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 4))) (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (pow (sin kx) 2))))))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(/ 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 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)))
(log (sin kx))
(+ (log (sin kx)) (* 1/2 (/ (pow ky 2) (pow (sin kx) 2))))
(+ (log (sin kx)) (* (pow ky 2) (+ (* 1/24 (* (pow ky 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4)))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(+ (log (sin kx)) (* (pow ky 2) (+ (* (pow ky 2) (+ (* 1/720 (* (pow ky 2) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 4))) (+ (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 30 (/ 1 (pow (sin kx) 6))))))) (* 1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))) (* 3 (/ 1 (pow (sin kx) 4))))))) (* 1/2 (/ 1 (pow (sin kx) 2))))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(+ (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 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 2/3 (pow ky 2)) 2)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/3 (* -4/45 (pow ky 2)))) 2)))
(- 1/2 (* 1/2 (cos (* 2 ky))))
(sin ky)
(* (sin ky) (sin th))
(cos (* 2 ky))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* -1/6 (pow th 2))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))))))))))
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(* 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 (* (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))
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 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)))
(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)))) (sin.f64 ky)) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1 binary64) (sin.f64 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)))
(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))))) (sin.f64 ky)) (*.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)))) (sin.f64 ky)))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (*.f64 kx kx) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(* -1 (log (sin ky)))
(neg.f64 (log.f64 (sin.f64 ky)))
(+ (* -1 (log (sin ky))) (* -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) (neg.f64 (log.f64 (sin.f64 ky))))
(+ (* -1 (log (sin ky))) (* (pow kx 2) (- (* -1/24 (* (pow kx 2) (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4)))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) (*.f64 kx kx)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -12 binary64) (/.f64 #s(literal -3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (neg.f64 (log.f64 (sin.f64 ky))))
(+ (* -1 (log (sin ky))) (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/24 (- (* -12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 3 (/ 1 (pow (sin ky) 4))))) (* -1/720 (* (pow kx 2) (+ (* 30 (/ 1 (pow (sin ky) 6))) (+ (* 180 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 4))) (* 360 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2)))) (pow (sin ky) 2))))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/720 binary64) (*.f64 kx kx)) (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)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2/45 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 360 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 4 binary64))) #s(literal 180 binary64) (/.f64 #s(literal 30 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (*.f64 (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 -12 binary64) (/.f64 #s(literal -3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) #s(literal -1/24 binary64))) (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (neg.f64 (log.f64 (sin.f64 ky))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky)))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 kx kx))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1/2 (* 1/2 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 2))) (* 3/4 (/ 1 (pow (- 1/2 (* 1/2 (cos (* 2 ky)))) 3))))))) (sqrt (- 1/2 (* 1/2 (cos (* 2 ky))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))) (*.f64 (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))) (*.f64 (*.f64 (*.f64 kx kx) (sin.f64 ky)) (*.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (sin.f64 th)))))) (*.f64 kx kx) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
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kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
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(/ (sin th) (sin ky))
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(log (sin ky))
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(sqrt (- 1/2 (* 1/2 (cos (* 2 ky)))))
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ky
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(- 1/2 (* 1/2 (cos (* 2 ky))))
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(* (sin ky) (sin th))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.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
(* 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))))
(*.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)
(* -1/6 (pow th 2))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky))))))))))))))
(*.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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64))))) (sin.f64 ky))) th)
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* 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))))))))))
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(* 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 (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)
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(*.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 (* (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)))

rewrite197.0ms (1.7%)

Memory
-37.7MiB live, 159.7MiB allocated; 15ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
060410
0101355
1348346
22295346
08883338
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
29 → 419
Calls
Call 1
Inputs
(*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th))
(*.f64 #s(literal -1/6 binary64) (*.f64 th 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)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky)))
#s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))))
(sin.f64 ky)
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(/.f64 (sin.f64 th) (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))))
(sin.f64 th)
(log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (sin.f64 th) (sin.f64 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 th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
#s(approx (sin kx) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))
(fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64))
Outputs
(*.f64 (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 ky)) (sin.f64 th))
(*.f64 (*.f64 (sin.f64 th) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(*.f64 (sin.f64 th) (*.f64 (sin.f64 ky) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (*.f64 (sin.f64 th) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 (*.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky))) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) #s(literal 2 binary64))
(/.f64 (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky)))) #s(literal 2 binary64))
(fma.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (sin.f64 th) (sin.f64 ky)) (*.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(fma.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))
(+.f64 (*.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (sin.f64 th) (sin.f64 ky))) (*.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(+.f64 (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))
(*.f64 (neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64))) (neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64))))
(*.f64 (fabs.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64))) (fabs.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) #s(literal -1 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 (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) #s(literal -1 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 ky) (sin.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 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal 1/2 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 ky) (sin.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 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 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 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 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 (fma.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))) #s(literal 4 binary64))
(/.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))) #s(literal 4 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(literal 2 binary64)) (*.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))))
(/.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) (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) (/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 #s(literal -1 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(sqrt.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64)))
(-.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sinh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(fabs.f64 (pow.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 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(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 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(+.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(+.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(*.f64 #s(literal -1/2 binary64) (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(*.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -2 binary64))))
(*.f64 #s(literal -1 binary64) (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (log.f64 (exp.f64 #s(literal -1 binary64))))
(*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(-.f64 (log.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(literal 3 binary64)))) (log.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) #s(literal 2 binary64)) (*.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sinh.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))))))
(-.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 (neg.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(-.f64 #s(literal 0 binary64) (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(+.f64 (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1/2 binary64))))
(log.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(*.f64 th (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (*.f64 (pow.f64 th #s(literal 9 binary64)) #s(literal -1/216 binary64)) (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (-.f64 (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 4 binary64))))) (*.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (-.f64 (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 4 binary64))))) (pow.f64 th #s(literal 3 binary64)))) (*.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (-.f64 (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 4 binary64))))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (-.f64 (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 4 binary64)))))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64)) th) (-.f64 (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/216 binary64) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))))
(/.f64 (*.f64 th (-.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64))) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 th (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal -1/216 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 th th) #s(literal -1/6 binary64)))))
(/.f64 (-.f64 (*.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (-.f64 th (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (*.f64 th (neg.f64 th)))) (neg.f64 (-.f64 (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)) th)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 th #s(literal 9 binary64)) #s(literal -1/216 binary64) (pow.f64 th #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (-.f64 (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 4 binary64)))))))
(/.f64 (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (*.f64 th (neg.f64 th))) (-.f64 (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)) th))
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(/.f64 (fma.f64 (pow.f64 th #s(literal 9 binary64)) #s(literal -1/216 binary64) (pow.f64 th #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)) (-.f64 (*.f64 th th) (*.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 4 binary64))))))
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eval174.0ms (1.5%)

Memory
-5.9MiB live, 142.8MiB allocated; 38ms collecting garbage
Compiler

Compiled 26 808 to 3 432 computations (87.2% saved)

prune187.0ms (1.6%)

Memory
20.2MiB live, 113.4MiB allocated; 5ms collecting garbage
Pruning

69 alts after pruning (64 fresh and 5 done)

PrunedKeptTotal
New65620676
Fresh44448
Picked325
Done033
Total66369732
Accuracy
100.0%
Counts
732 → 69
Alt Table
Click to see full alt table
StatusAccuracyProgram
81.8%
(/.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)))
47.2%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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)))
14.2%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
48.6%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
19.4%
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
81.6%
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (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)))))) (sin.f64 th))
81.5%
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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)))
70.9%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))
✓99.6%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
44.9%
(*.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)))
24.8%
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
46.4%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
24.1%
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
42.5%
(*.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)))
29.4%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
32.8%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
81.6%
(*.f64 (/.f64 (sin.f64 ky) (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)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))
22.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
43.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
31.6%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
81.9%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))) (sin.f64 th))
33.3%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
52.0%
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
28.0%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
81.6%
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th))
81.6%
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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)))
31.6%
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
33.2%
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
27.4%
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
18.1%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
28.7%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
33.2%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
25.5%
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
42.6%
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
32.9%
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
27.3%
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
40.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
25.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 #s(approx (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (neg.f64 (log.f64 (sin.f64 kx))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
16.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
7.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
17.0%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
✓29.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
45.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
14.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
✓17.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
26.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
10.8%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
10.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
28.3%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
11.4%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
11.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
15.6%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
16.2%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
16.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
✓24.1%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
11.6%
#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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th th) th) #s(literal -1/6 binary64) th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
✓11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
11.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
11.3%
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
11.6%
#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)))
9.9%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
4.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
42.5%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
42.7%
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
Compiler

Compiled 5 820 to 2 269 computations (61% saved)

regimes292.0ms (2.5%)

Memory
20.5MiB live, 446.9MiB allocated; 44ms collecting garbage
Counts
105 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (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)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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 (/.f64 (*.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (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)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #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) (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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 #s(approx (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (neg.f64 (log.f64 (sin.f64 kx))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#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) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (*.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))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
(/.f64 (*.f64 (sin.f64 th) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 kx))) (sqrt.f64 (neg.f64 (sin.f64 kx))))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (neg.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 2 binary64)) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 kx))) (sqrt.f64 (neg.f64 (sin.f64 kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 (*.f64 (log.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (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 (*.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 ky))) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 1/4 binary64))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (*.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)))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Calls

9 calls:

57.0ms
(/.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)))))
34.0ms
th
29.0ms
ky
29.0ms
(sin.f64 th)
29.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
99.7%1(sin.f64 th)
99.7%1(sin.f64 kx)
99.7%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.7%1(sin.f64 ky)
99.7%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.7%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.7%1kx
99.7%1ky
99.7%1th
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes254.0ms (2.2%)

Memory
-8.2MiB live, 408.1MiB allocated; 47ms collecting garbage
Counts
82 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (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)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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 (/.f64 (*.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (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)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #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) (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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (exp.f64 #s(approx (* (log (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) -1) (neg.f64 (log.f64 (sin.f64 kx))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
Outputs
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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

9 calls:

29.0ms
(*.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))
28.0ms
(sin.f64 th)
23.0ms
kx
23.0ms
ky
22.0ms
th
Results
AccuracySegmentsBranch
91.3%3(sin.f64 th)
99.4%3(sin.f64 kx)
99.4%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.0%3(sin.f64 ky)
98.8%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)))))
90.8%5(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.4%2kx
99.0%2ky
91.3%2th
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes433.0ms (3.7%)

Memory
-35.4MiB live, 129.6MiB allocated; 787ms collecting garbage
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) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (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)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))
(*.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (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 (/.f64 (*.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))) (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)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #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 th) (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)))) (sin.f64 ky))
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th))
Calls

2 calls:

402.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
26.0ms
kx
Results
AccuracySegmentsBranch
99.2%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.2%2kx
Compiler

Compiled 5 to 9 computations (-80% saved)

regimes57.0ms (0.5%)

Memory
-39.5MiB live, 115.2MiB allocated; 17ms collecting garbage
Counts
73 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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)))
Outputs
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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)))
Calls

2 calls:

20.0ms
kx
18.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
99.2%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.2%2kx
Compiler

Compiled 5 to 9 computations (-80% saved)

regimes199.0ms (1.7%)

Memory
7.7MiB live, 339.5MiB allocated; 49ms collecting garbage
Counts
72 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 ky))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
Calls

9 calls:

37.0ms
(sin.f64 th)
23.0ms
(*.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))
21.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
20.0ms
(sin.f64 kx)
20.0ms
kx
Results
AccuracySegmentsBranch
69.7%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))
76.4%3(sin.f64 th)
79.0%3th
86.9%5(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
77.5%4(sin.f64 ky)
78.5%4(sin.f64 kx)
76.2%2ky
75.9%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
76.1%2kx
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes24.0ms (0.2%)

Memory
-6.7MiB live, 38.0MiB allocated; 5ms collecting garbage
Counts
71 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
#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) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (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) ky)) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(literal 1/2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (*.f64 (sqrt.f64 (neg.f64 (sin.f64 ky))) (sqrt.f64 (neg.f64 (sin.f64 ky)))))))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.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 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
Calls

1 calls:

20.0ms
(/.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
86.9%5(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes19.0ms (0.2%)

Memory
34.2MiB live, 34.2MiB allocated; 0ms collecting garbage
Counts
64 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Outputs
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.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 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
Calls

1 calls:

15.0ms
(/.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
86.8%5(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes22.0ms (0.2%)

Memory
-1.3MiB live, 43.9MiB allocated; 4ms collecting garbage
Counts
62 → 5
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
Outputs
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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)))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky))
Calls

1 calls:

18.0ms
(/.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
85.0%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 13 to 11 computations (15.4% saved)

regimes24.0ms (0.2%)

Memory
4.1MiB live, 52.3MiB allocated; 11ms collecting garbage
Counts
61 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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)))
(*.f64 (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
Calls

1 calls:

20.0ms
(/.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
85.2%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)

regimes25.0ms (0.2%)

Memory
-34.3MiB live, 57.4MiB allocated; 12ms collecting garbage
Counts
60 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
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
85.2%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)

regimes22.0ms (0.2%)

Memory
7.5MiB live, 53.1MiB allocated; 8ms collecting garbage
Counts
56 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 #s(approx (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx)))) (-.f64 (fma.f64 (*.f64 ky ky) #s(literal 2 binary64) #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 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 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64))) (sin.f64 th)) (sin.f64 ky)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
Calls

1 calls:

14.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
85.1%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)

regimes123.0ms (1%)

Memory
5.3MiB live, 194.8MiB allocated; 28ms collecting garbage
Counts
51 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) (sin.f64 th))
Outputs
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) 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 ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
Calls

8 calls:

18.0ms
(sin.f64 kx)
17.0ms
th
17.0ms
kx
17.0ms
(sin.f64 ky)
13.0ms
ky
Results
AccuracySegmentsBranch
72.0%3(sin.f64 ky)
51.0%2(sin.f64 th)
72.1%4(sin.f64 kx)
72.0%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
72.1%3kx
72.2%2ky
54.7%3th
73.9%4(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 26 to 38 computations (-46.2% saved)

regimes139.0ms (1.2%)

Memory
-5.3MiB live, 139.9MiB allocated; 15ms collecting garbage
Counts
47 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (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 ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))
Outputs
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
Calls

7 calls:

47.0ms
(/.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
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
16.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
12.0ms
kx
12.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
58.0%5(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
69.3%4(sin.f64 kx)
66.8%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
63.6%4(sin.f64 ky)
67.0%3kx
68.1%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)))))
63.6%3ky
Compiler

Compiled 39 to 44 computations (-12.8% saved)

regimes54.0ms (0.5%)

Memory
-12.0MiB live, 95.0MiB allocated; 12ms collecting garbage
Counts
43 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (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 #s(approx (* (sin th) (sin ky)) (*.f64 #s(approx (* (+ (* (* ky ky) -1/6) 1) (sin th)) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (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

4 calls:

16.0ms
(/.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
kx
11.0ms
(sin.f64 kx)
10.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
65.6%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)))))
60.3%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
60.4%2kx
63.0%3(sin.f64 kx)
Compiler

Compiled 20 to 24 computations (-20% saved)

regimes63.0ms (0.5%)

Memory
22.6MiB live, 115.1MiB allocated; 3ms collecting garbage
Counts
38 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (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

6 calls:

11.0ms
kx
11.0ms
(sin.f64 kx)
10.0ms
(sin.f64 ky)
10.0ms
ky
9.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
49.3%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
49.3%3kx
56.9%4(sin.f64 ky)
51.3%3(sin.f64 kx)
48.5%3ky
58.8%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 23 to 31 computations (-34.8% saved)

regimes10.0ms (0.1%)

Memory
15.1MiB live, 15.1MiB allocated; 0ms collecting garbage
Counts
32 → 4
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(approx (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 (cos.f64 (fma.f64 #s(literal -2 binary64) ky (PI.f64))) #s(literal 1 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 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))
Calls

1 calls:

8.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
58.7%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)

regimes39.0ms (0.3%)

Memory
-22.1MiB live, 24.7MiB allocated; 2ms collecting garbage
Counts
28 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (*.f64 ky ky) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (sin.f64 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

2 calls:

29.0ms
(/.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)))))
8.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
53.9%3(sin.f64 ky)
55.2%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 15 to 15 computations (0% saved)

regimes73.0ms (0.6%)

Memory
14.9MiB live, 109.3MiB allocated; 8ms collecting garbage
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) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.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 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 #s(literal 1 binary64) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) #s(approx (/ 1 (sin ky)) (/.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/6 binary64) #s(literal 1 binary64)) ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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

9 calls:

14.0ms
(sin.f64 ky)
10.0ms
kx
7.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
7.0ms
(sin.f64 th)
7.0ms
th
Results
AccuracySegmentsBranch
44.3%2ky
37.7%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
37.8%2kx
37.4%2(sin.f64 kx)
31.4%2(sin.f64 th)
44.4%2(sin.f64 ky)
33.1%2th
39.8%3(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
45.6%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 42 to 51 computations (-21.4% saved)

regimes20.0ms (0.2%)

Memory
-7.9MiB live, 35.9MiB allocated; 4ms collecting garbage
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) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
Outputs
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

3 calls:

8.0ms
(sin.f64 ky)
5.0ms
ky
5.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
41.1%2ky
41.2%2(sin.f64 ky)
43.9%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 16 to 18 computations (-12.5% saved)

regimes53.0ms (0.4%)

Memory
-6.1MiB live, 92.2MiB allocated; 9ms collecting garbage
Counts
18 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 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)) (-.f64 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (sqrt.f64 th) (sqrt.f64 th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#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 (*.f64 th th) #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 ky ky) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

9 calls:

9.0ms
th
6.0ms
ky
5.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
5.0ms
(sin.f64 ky)
5.0ms
kx
Results
AccuracySegmentsBranch
24.1%1(sin.f64 th)
27.2%2th
24.1%1(sin.f64 kx)
25.8%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
25.8%2kx
29.9%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))
28.0%2ky
28.3%2(sin.f64 ky)
29.8%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)

regimes17.0ms (0.1%)

Memory
30.4MiB live, 30.4MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.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)) (sin.f64 th))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
Calls

7 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)))))
2.0ms
(sin.f64 ky)
2.0ms
kx
2.0ms
ky
Results
AccuracySegmentsBranch
24.1%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
24.1%1kx
24.1%1th
24.1%1ky
24.1%1(sin.f64 ky)
24.1%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))
24.1%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 38 to 43 computations (-13.2% saved)

regimes27.0ms (0.2%)

Memory
-9.3MiB live, 36.7MiB allocated; 3ms collecting garbage
Accuracy

Total -0.4b remaining (-0.7%)

Threshold costs -0.4b (-0.7%)

Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 th th) (*.f64 th #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 (*.f64 th 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 (*.f64 (*.f64 th th) #s(literal 1/120 binary64)) #s(literal 1/6 binary64)) (*.f64 th th) #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) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
Calls

9 calls:

10.0ms
(sin.f64 kx)
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
kx
2.0ms
(sin.f64 ky)
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
11.7%1ky
11.7%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
11.7%1(sin.f64 ky)
11.7%1(sin.f64 th)
11.7%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))
11.7%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)))))
11.7%1kx
11.7%1(sin.f64 kx)
11.7%1th
Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch26.0ms (0.2%)

Memory
-16.0MiB live, 29.2MiB allocated; 4ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
24.0ms
2.1259492397790992e-10
1.3517983047073442e-6
Samples
15.0ms128×0valid
Compiler

Compiled 379 to 306 computations (19.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sin: 6.0ms (50.5% of total)
ival-pow2: 2.0ms (16.8% of total)
ival-div: 1.0ms (8.4% of total)
ival-add: 1.0ms (8.4% of total)
ival-mult: 1.0ms (8.4% of total)
ival-sqrt: 1.0ms (8.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory
2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
2.1259492397790992e-10
1.3517983047073442e-6
Compiler

Compiled 363 to 314 computations (13.5% saved)

bsearch2.0ms (0%)

Memory
2.5MiB live, 2.5MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
1.0ms
2.1259492397790992e-10
1.3517983047073442e-6
Compiler

Compiled 363 to 314 computations (13.5% saved)

bsearch1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999977582
1.0
0.0ms
0.03303359963748521
0.09056959290129228
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.6MiB live, 1.6MiB allocated; 0ms collecting garbage
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999977582
1.0
0.0ms
0.0017552130964830941
0.03303359963748521
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.5MiB live, 1.5MiB allocated; 0ms collecting garbage
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9999999999977582
1.0
0.0ms
0.0017552130964830941
0.03303359963748521
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.6MiB live, 1.7MiB allocated; 0ms collecting garbage
Algorithm
4×left-value
Steps
TimeLeftRight
0.0ms
0.9770224406858729
0.9864946525966641
0.0ms
1.032680322263824e-5
0.0017552130964830941
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
+inf
0.0ms
0.9658533647176324
0.9770224406858729
0.0ms
1.032680322263824e-5
0.0017552130964830941
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated; 0ms collecting garbage
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
+inf
0.0ms
0.9658533647176324
0.9770224406858729
0.0ms
1.032680322263824e-5
0.0017552130964830941
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
+inf
0.0ms
0.9658533647176324
0.9770224406858729
0.0ms
0.09056959290129228
0.22164887191857335
0.0ms
-0.05221335763689253
5.3668796113938245e-303
0.0ms
-1.0
-0.9691966512473584
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch39.0ms (0.3%)

Memory
-5.1MiB live, 40.1MiB allocated; 5ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
37.0ms
1.457085980634638
1207.7835289004108
Samples
18.0ms128×0valid
Compiler

Compiled 611 to 402 computations (34.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-sin: 10.0ms (66.7% of total)
ival-pow2: 2.0ms (13.3% of total)
ival-div: 1.0ms (6.7% of total)
ival-add: 1.0ms (6.7% of total)
ival-mult: 1.0ms (6.7% of total)
ival-sqrt: 1.0ms (6.7% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated; 0ms collecting garbage
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
1.3517983047069325e-6
0.007134642183612938
0.0ms
1.2502185417002428e-167
2.7696625916958123e-165
0.0ms
-0.007595987810611232
1.5450124067395034e-307
Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated; 0ms collecting garbage
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.09056959290129228
0.22164887191857335
0.0ms
2.410642586807721e-193
5.4898451395524445e-192
0.0ms
-0.05221335763689253
5.3668796113938245e-303
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.09056959290129228
0.22164887191857335
0.0ms
2.410642586807721e-193
5.4898451395524445e-192
0.0ms
-0.12528857803689902
-0.05221335763689253
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Algorithm
3×left-value
Steps
TimeLeftRight
0.0ms
0.09056959290129228
0.22164887191857335
0.0ms
2.410642586807721e-193
5.4898451395524445e-192
0.0ms
-0.12528857803689902
-0.05221335763689253
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated; 0ms collecting garbage
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.09056959290129228
0.22164887191857335
0.0ms
-0.12528857803689902
-0.05221335763689253
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.09056959290129228
0.22164887191857335
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.09056959290129228
0.22164887191857335
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
4.439391379800535e-92
1.2976889958795679e-90
Compiler

Compiled 19 to 19 computations (0% saved)

simplify112.0ms (1%)

Memory
-16.9MiB live, 121.7MiB allocated; 22ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02542675
13242675
24762663
37992663
415892663
533702663
668802663
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 kx #s(literal 6375194751874021/4722366482869645213696 binary64)) (*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky)) (*.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 kx #s(literal 6375194751874021/4722366482869645213696 binary64)) (*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky)) (*.f64 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th)))
(if (<=.f64 kx #s(literal 6375194751874021/4722366482869645213696 binary64)) (*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky)) (*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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))))
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(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/1152921504606846976 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))))) (if (<=.f64 (sin.f64 kx) #s(literal 5311379928167671/265568996408383549344794103276234313664796558863515961599722069100201779930426121369581251132614642834444664743123250507673289668826353619704759989383293675971915635417696609515864064 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 (sin.f64 th) (fabs.f64 (sin.f64 ky))))) (if (<=.f64 (sin.f64 kx) #s(literal 4722366482869645/2361183241434822606848 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (- 1/2 (* (cos (* 2 ky)) 1/2)) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)))))
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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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (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 4109481173084667/10273702932711667006330058365000251299903007427389011444332579888806117488861485980690754953667164943802701111047223081470741078613640241920171513223929454785068796232672743355843093277117817807170494632296448 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #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 3602879701896397/36028797018963968 binary64)) (*.f64 #s(approx (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (/.f64 (sin.f64 th) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (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 4109481173084667/10273702932711667006330058365000251299903007427389011444332579888806117488861485980690754953667164943802701111047223081470741078613640241920171513223929454785068796232672743355843093277117817807170494632296448 binary64)) #s(approx (* (/ (sin ky) (/ (sqrt (+ (- 1 (cos (* 2 ky))) (- 1 (cos (* 2 kx))))) (sqrt 2))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (*.f64 (sin.f64 th) ky) (sqrt.f64 #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 3602879701896397/36028797018963968 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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (fabs.f64 (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 3602879701896397/36028797018963968 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 3602879701896397/36028797018963968 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 3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (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 7339195571168229/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) #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)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 kx #s(literal 6375194751874021/4722366482869645213696 binary64)) (*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky)) (*.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 kx #s(literal 6375194751874021/4722366482869645213696 binary64)) (*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky)) (*.f64 (*.f64 (/.f64 (sin.f64 ky) (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))) (sin.f64 th)))
(if (<=.f64 kx #s(literal 6375194751874021/4722366482869645213696 binary64)) (*.f64 (/.f64 (sin.f64 th) (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)))) (sin.f64 ky)) (*.f64 (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (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))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin ky) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 ky ky)) #s(literal 1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (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 281474976710025/281474976710656 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (/.f64 (sin.f64 th) (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)))) (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 -1 binary64)) (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1152921504606847/576460752303423488 binary64)) (*.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 281474976710025/281474976710656 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (/.f64 (sin.f64 th) (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)))) (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 3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin 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 7339195571168229/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 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 7339195571168229/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936 binary64)) #s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) #s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))
#s(approx (* (/ (sin th) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky)) #s(approx (sin th) (fma.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 th th)) th th)))

derivations1.8s (15.5%)

Memory
39.5MiB live, 1 126.4MiB allocated; 128ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08275514
131575185
081414948
035204
057179
1183179
21188175
08684175
01349
02249
15949
231949
3312949
0893734
060410
0101355
1348346
22295346
08883338
054325
089272
1309272
22277261
09847261
06934135
125053910
081663660
04482190
116192098
275092072
082991959
03171402
111341336
252361308
084061228
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×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
Compiler

Compiled 2 734 to 258 computations (90.6% saved)

preprocess208.0ms (1.8%)

Memory
-0.7MiB live, 277.0MiB allocated; 41ms collecting garbage
Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 5 698 to 704 computations (87.6% saved)

end0.0ms (0%)

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

Profiling

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