Toniolo and Linder, Equation (3b), real

Time bar (total: 11.1s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze191.0ms (1.7%)

Memory
-8.0MiB live, 309.1MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
0%0%99.9%0.1%0%0%0%3
0%0%99.9%0.1%0%0%0%4
25%25%74.9%0.1%0%0%0%5
43.8%43.7%56.2%0.1%0%0%0%6
43.8%43.7%56.2%0.1%0%0%0%7
53.1%53%46.8%0.1%0%0%0%8
60.9%60.8%39%0.1%0%0%0%9
60.9%60.8%39%0.1%0%0%0%10
64.8%64.7%35.1%0.1%0%0%0%11
68.4%68.3%31.6%0.1%0%0%0%12
Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.8s (16.6%)

Memory
7.3MiB live, 2 678.0MiB allocated
Samples
1.5s8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.2s
ival-sin: 674.0ms (56.9% of total)
ival-pow2: 252.0ms (21.3% of total)
ival-mult: 82.0ms (6.9% of total)
ival-sqrt: 77.0ms (6.5% of total)
ival-div: 50.0ms (4.2% of total)
ival-add: 40.0ms (3.4% of total)
ival-true: 7.0ms (0.6% of total)
ival-assert: 3.0ms (0.3% of total)
Bogosity

explain351.0ms (3.2%)

Memory
16.3MiB live, 335.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
150-2(1.6123248050070914e-158 -2.140424709825568e-264 -2.9219464755304866e-113)(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-rescue130
↳(pow.f64 (sin.f64 kx) #s(literal 2 binary64))underflow67
↳(pow.f64 (sin.f64 ky) #s(literal 2 binary64))underflow48
↳(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))underflow13
Confusion
Predicted +Predicted -
+132
-0241
Precision
1.0
Recall
0.8666666666666667
Confusion?
Predicted +Predicted MaybePredicted -
+1302
-00241
Precision?
1.0
Recall?
0.8666666666666667
Freqs
test
numberfreq
0243
113
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
169.0ms512×0valid
Compiler

Compiled 218 to 56 computations (74.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-sin: 50.0ms (53.5% of total)
ival-pow2: 30.0ms (32.1% of total)
ival-div: 3.0ms (3.2% of total)
ival-mult: 3.0ms (3.2% of total)
ival-sqrt: 3.0ms (3.2% of total)
ival-add: 2.0ms (2.1% of total)
ival-true: 1.0ms (1.1% of total)
ival-assert: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess277.0ms (2.5%)

Memory
-31.9MiB live, 204.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045153
1103147
2267147
3615147
41916147
56265147
01316
02216
13016
25016
311416
434016
5129216
6336016
7654016
0800611
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶94.4%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

localize74.0ms (0.7%)

Memory
23.6MiB live, 66.6MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.16796875
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy0.2506637695368841
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy0.29591752930532605
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy3.384731532291253
(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 134 to 28 computations (79.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-sin: 17.0ms (39.3% of total)
ival-sqrt: 17.0ms (39.3% of total)
ival-pow2: 5.0ms (11.6% of total)
ival-div: 2.0ms (4.6% of total)
ival-mult: 2.0ms (4.6% of total)
ival-add: 1.0ms (2.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series90.0ms (0.8%)

Memory
-7.1MiB live, 29.8MiB allocated
Counts
4 → 28
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))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #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))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin kx) 2)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(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))))
(pow (sin ky) 2)
Calls

9 calls:

TimeVariablePointExpression
76.0ms
kx
@-inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
4.0ms
ky
@0
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.0ms
kx
@inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.0ms
kx
@0
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
2.0ms
ky
@inf
((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))

simplify638.0ms (5.8%)

Memory
4.8MiB live, 193.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0208700
1710685
23162660
08290608
Stop Event
1×iter limit
1×node limit
Counts
28 → 28
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))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin kx) 2)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(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))))
(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)))
(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)) (fma.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)) (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx))
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) (*.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 kx kx) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))) (-.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))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(* (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))
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (/.f64 (fma.f64 (*.f64 ky ky) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) #s(literal 1/2 binary64)) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (/.f64 (fma.f64 (*.f64 (*.f64 ky ky) #s(literal 1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.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)) (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (*.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky))
(/ 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)) (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 (/.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)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.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))))) (*.f64 #s(literal -1/12 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 (/.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) (+.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 (/.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)))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))

rewrite175.0ms (1.6%)

Memory
17.2MiB live, 214.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01031
01731
15531
234131
3356931
0822921
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 261
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))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Outputs
(*.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)) (/.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 1 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 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (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 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (pow.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 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (pow.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)))) #s(literal -1 binary64)))
(*.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (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 binary64))))
(*.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 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 #s(literal -1 binary64) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64))) #s(literal -1 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 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)) #s(literal -1 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 #s(literal -1 binary64) (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 6 binary64)) (pow.f64 (sin.f64 kx) #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 ky) (sin.f64 kx)) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (*.f64 (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 (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 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 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)))) #s(literal 1 binary64)))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal -1 binary64))
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 1 binary64))
(neg.f64 (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(fabs.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (sin.f64 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))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(exp.f64 (*.f64 (log.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)))
(exp.f64 (*.f64 (log.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)))
(exp.f64 (*.f64 (log.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)))
(exp.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(+.f64 (cosh.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sinh.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 ky))
(*.f64 (*.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 ky))) (sqrt.f64 (sin.f64 ky)))
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(*.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 ky))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1 binary64))
(*.f64 (sin.f64 ky) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1 binary64))
(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1 binary64))
(/.f64 (/.f64 (neg.f64 (sin.f64 ky)) #s(literal -1 binary64)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(/.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)))
(/.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1 binary64)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(literal 1 binary64))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(exp.f64 (-.f64 (log.f64 (sin.f64 ky)) (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (-.f64 (log.f64 (sin.f64 ky)) (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sinh.f64 (-.f64 (log.f64 (sin.f64 ky)) (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
(+.f64 (cosh.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(literal -1 binary64))) (sinh.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(literal -1 binary64))))

eval87.0ms (0.8%)

Memory
9.6MiB live, 170.1MiB allocated
Compiler

Compiled 7 735 to 1 942 computations (74.9% saved)

prune24.0ms (0.2%)

Memory
-25.7MiB live, 62.6MiB allocated
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New26821289
Fresh000
Picked101
Done000
Total26921290
Accuracy
100.0%
Counts
290 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.7%
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
93.7%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64))))) (sin.f64 th))
33.5%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (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))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
71.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶85.6%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
▶86.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
▶38.8%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
87.6%
(*.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))
23.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (exp.f64 (*.f64 (log.f64 (neg.f64 (sin.f64 kx))) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
54.1%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
29.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
69.6%
(*.f64 (*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64))) (sin.f64 th))
94.1%
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64))) (sin.f64 th))
87.7%
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))))) (sin.f64 th))
99.5%
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
69.3%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
25.1%
(*.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))
25.5%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
93.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
▶30.9%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
Compiler

Compiled 904 to 680 computations (24.8% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

localize206.0ms (1.9%)

Memory
14.0MiB live, 364.3MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.3125
(*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))
accuracy0.31640625
(*.f64 (cos.f64 ky) (cos.f64 ky))
accuracy3.384731532291253
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
accuracy13.075849564519794
(-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64))))
accuracy0.2506637695368841
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy0.31640625
(*.f64 (cos.f64 ky) (cos.f64 ky))
accuracy3.384731532291253
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
accuracy13.098128505207043
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
accuracy0.16796875
(/.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)))))
accuracy0.2506637695368841
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy3.384731532291253
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
accuracy36.45408182240971
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
accuracy0.0
(sin.f64 th)
accuracy0.14453125
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
accuracy44.59955543640338
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64))
accuracy0.0078125
(sin.f64 ky)
accuracy0.078125
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.14453125
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
accuracy0.16796875
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
Samples
65.0ms157×0valid
52.0ms63×1valid
47.0ms36×2valid
Compiler

Compiled 897 to 86 computations (90.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 123.0ms
ival-cos: 36.0ms (29.3% of total)
ival-sin: 22.0ms (17.9% of total)
ival-mult: 20.0ms (16.3% of total)
ival-div: 11.0ms (8.9% of total)
adjust: 7.0ms (5.7% of total)
ival-sqrt: 7.0ms (5.7% of total)
ival-pow2: 6.0ms (4.9% of total)
ival-add: 5.0ms (4.1% of total)
ival-hypot: 5.0ms (4.1% of total)
ival-sub: 4.0ms (3.3% of total)
exact: 1.0ms (0.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series83.0ms (0.8%)

Memory
-19.7MiB live, 82.5MiB allocated
Counts
17 → 73
Calls
Call 1
Inputs
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 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)))) #s(literal 1 binary64))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
(sin.f64 th)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(*.f64 (cos.f64 ky) (cos.f64 ky))
(-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))
Outputs
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 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin kx) 2)
(sqrt (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))
(sqrt (- (+ (* 1/4 (/ 1 (pow (cos ky) 2))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(/ (* 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 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
(* 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))))
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(* (pow ky 2) (+ 1 (* -4/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 32/45 (pow ky 2)) 4/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 32/45 (* -64/315 (pow ky 2)))) 4/3))))
1/4
(+ 1/4 (* -1 (pow ky 2)))
(+ 1/4 (* (pow ky 2) (- (* 4/3 (pow ky 2)) 1)))
(+ 1/4 (* (pow ky 2) (- (* (pow ky 2) (+ 4/3 (* -32/45 (pow ky 2)))) 1)))
(pow (sin ky) 2)
(- 1 (pow (cos ky) 2))
(pow (cos ky) 2)
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(* 1/4 (pow (cos (* 2 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))))
Calls

9 calls:

TimeVariablePointExpression
47.0ms
ky
@inf
((/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (* (cos ky) (cos ky))))) (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2)))
11.0ms
kx
@inf
((/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (* (cos ky) (cos ky))))) (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2)))
5.0ms
ky
@-inf
((/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (* (cos ky) (cos ky))))) (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2)))
4.0ms
kx
@0
((/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (* (cos ky) (cos ky))))) (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2)))
4.0ms
kx
@-inf
((/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (pow (sin ky) 2) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2))) (* (cos ky) (cos ky))))) (* (* (cos (* ky 2)) 1/2) (* (cos (* ky 2)) 1/2)))

simplify175.0ms (1.6%)

Memory
6.3MiB live, 160.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04512170
116121993
274091920
082891779
Stop Event
1×iter limit
1×node limit
Counts
73 → 71
Calls
Call 1
Inputs
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 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))))))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin kx) 2)
(sqrt (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))
(sqrt (- (+ (* 1/4 (/ 1 (pow (cos ky) 2))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(/ (* 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 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
(* 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))))
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(* (pow ky 2) (+ 1 (* -4/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 32/45 (pow ky 2)) 4/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 32/45 (* -64/315 (pow ky 2)))) 4/3))))
1/4
(+ 1/4 (* -1 (pow ky 2)))
(+ 1/4 (* (pow ky 2) (- (* 4/3 (pow ky 2)) 1)))
(+ 1/4 (* (pow ky 2) (- (* (pow ky 2) (+ 4/3 (* -32/45 (pow ky 2)))) 1)))
(pow (sin ky) 2)
(- 1 (pow (cos ky) 2))
(pow (cos ky) 2)
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(* 1/4 (pow (cos (* 2 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))))
Outputs
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 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 (sin.f64 th) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (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 (sin.f64 th) (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 (sin.f64 th) (-.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (/.f64 #s(literal -3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx) (/.f64 (*.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
(sin 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))
(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 (fma.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 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)
(sqrt (- 1 (pow (cos ky) 2)))
(fabs.f64 (sin.f64 ky))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fabs.f64 (sin.f64 ky)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (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)) (*.f64 kx kx) #s(literal 1/2 binary64))) (*.f64 kx kx) (fabs.f64 (sin.f64 ky)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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)))) (*.f64 kx kx) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (*.f64 kx kx) (fabs.f64 (sin.f64 ky)))
(sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))
(sqrt.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))) (sqrt.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (*.f64 kx kx) #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))
(+ (sqrt (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2))))))) (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (pow (cos ky) 2))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (fma.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)))) (*.f64 kx kx) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))
(* (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))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sqrt (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (- (+ (* 1/4 (/ 1 (pow (cos ky) 2))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (pow (cos ky) 2)))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (/.f64 (fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))))
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(fma.f64 (*.f64 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 -1/2 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 #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 (/.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 (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 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (-.f64 (/.f64 #s(literal 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 (+ (* (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 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (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 (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))))
(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 (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
(* 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)) (fma.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)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 ky ky) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) ky)
(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 (fma.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 (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (*.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)
(+ 1 (* -1 (pow ky 2)))
(-.f64 #s(literal 1 binary64) (*.f64 ky ky))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/3 binary64) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (*.f64 ky ky) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(* (pow ky 2) (+ 1 (* -4/3 (pow ky 2))))
(*.f64 (*.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 32/45 (pow ky 2)) 4/3))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 32/45 binary64) (*.f64 ky ky) #s(literal -4/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 32/45 (* -64/315 (pow ky 2)))) 4/3))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -64/315 binary64) (*.f64 ky ky) #s(literal 32/45 binary64)) (*.f64 ky ky) #s(literal -4/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1 (pow ky 2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 ky ky))
(+ 1/4 (* (pow ky 2) (- (* 4/3 (pow ky 2)) 1)))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 ky ky) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1/4 binary64))
(+ 1/4 (* (pow ky 2) (- (* (pow ky 2) (+ 4/3 (* -32/45 (pow ky 2)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -32/45 binary64) (*.f64 ky ky) #s(literal 4/3 binary64)) (*.f64 ky ky) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1/4 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(- 1 (pow (cos ky) 2))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (cos ky) 2)
(pow.f64 (cos.f64 ky) #s(literal 2 binary64))
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(* 1/4 (pow (cos (* 2 ky)) 2))
(*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 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))))))))))
(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))))) (fma.f64 (*.f64 (*.f64 (sin.f64 ky) th) th) #s(literal 1/120 binary64) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (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 (*.f64 (*.f64 th th) (*.f64 th th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 (*.f64 (*.f64 (sin.f64 ky) th) th) #s(literal -1/5040 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)) (fma.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)) (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) th)

rewrite167.0ms (1.5%)

Memory
19.9MiB live, 215.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041184
070130
1279130
22613130
08243129
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
17 → 888
Calls
Call 1
Inputs
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 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)))) #s(literal 1 binary64))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
(sin.f64 th)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(*.f64 (cos.f64 ky) (cos.f64 ky))
(-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))
Outputs
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 ky))
(*.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal -1 binary64))
(/.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64)) (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 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))
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(*.f64 (sqrt.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 4 binary64))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(*.f64 (sqrt.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 3 binary64)))) (sqrt.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 3 binary64)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 3 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 3 binary64)))))
(*.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(*.f64 (sqrt.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (sqrt.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))))
(*.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (neg.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))))
(*.f64 (fabs.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(*.f64 (fabs.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (fabs.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))))
(*.f64 (*.f64 #s(literal 1/4 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))
(*.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))
(*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64))))
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/4 binary64)))
(*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (*.f64 #s(literal 1/4 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))
(*.f64 #s(literal 1/4 binary64) (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 4 binary64)) #s(literal 1/16 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 2 binary64))
(neg.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(sqrt.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 4 binary64)) #s(literal 1/16 binary64)))
(fabs.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(fabs.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) #s(literal 2 binary64))))

eval205.0ms (1.8%)

Memory
-4.5MiB live, 379.5MiB allocated
Compiler

Compiled 39 354 to 6 067 computations (84.6% saved)

prune47.0ms (0.4%)

Memory
-15.3MiB live, 107.3MiB allocated
Pruning

30 alts after pruning (29 fresh and 1 done)

PrunedKeptTotal
New1 223211 244
Fresh8816
Picked415
Done000
Total1 235301 265
Accuracy
100.0%
Counts
1 265 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.6%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
▶99.7%
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
39.7%
(*.f64 (/.f64 (/.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))) (sin.f64 th))
49.2%
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
29.9%
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
79.4%
(*.f64 (/.f64 (sin.f64 ky) (/.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))) (sin.f64 th))
79.2%
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
✓38.8%
(*.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))
32.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
32.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
▶37.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
16.7%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
54.1%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
25.2%
(*.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))
29.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
▶48.1%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
▶99.6%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
38.7%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
38.7%
(*.f64 (*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 ky)) (sin.f64 th))
99.5%
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
69.3%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
99.6%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
25.1%
(*.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))
25.5%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
93.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
17.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
16.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
25.1%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
45.5%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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)))))))
▶30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Compiler

Compiled 1 338 to 1 039 computations (22.3% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

localize174.0ms (1.6%)

Memory
23.8MiB live, 217.3MiB allocated
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy0.078125
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy0.14453125
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
accuracy0.15625
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
accuracy0.171875
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
accuracy0.31640625
(*.f64 (cos.f64 ky) (cos.f64 ky))
accuracy3.384731532291253
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
accuracy13.098128505207043
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
accuracy31.462988182134428
#s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx))
accuracy0.0078125
(sin.f64 ky)
accuracy0.14453125
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
accuracy0.16796875
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
accuracy33.325292217149844
#s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))
accuracy0.0
(sin.f64 th)
accuracy44.24692519517099
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
accuracy0.0078125
(sin.f64 ky)
accuracy0.078125
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy0.139003759768442
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
accuracy0.15625
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
Samples
75.0ms157×0valid
40.0ms63×1valid
31.0ms36×2valid
Compiler

Compiled 666 to 82 computations (87.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 101.0ms
ival-sin: 22.0ms (21.9% of total)
ival-cos: 17.0ms (16.9% of total)
ival-mult: 16.0ms (15.9% of total)
ival-div: 12.0ms (11.9% of total)
ival-hypot: 10.0ms (9.9% of total)
adjust: 5.0ms (5% of total)
const: 5.0ms (5% of total)
ival-pow2: 5.0ms (5% of total)
ival-sqrt: 3.0ms (3% of total)
ival-add: 3.0ms (3% of total)
ival-sub: 2.0ms (2% of total)
ival-fabs: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series54.0ms (0.5%)

Memory
2.8MiB live, 43.0MiB allocated
Counts
17 → 80
Calls
Call 1
Inputs
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(sin.f64 th)
#s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
#s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(*.f64 (cos.f64 ky) (cos.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
Outputs
1
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(+ 1 (* -1/2 (/ (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))))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (* (sin ky) (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 (cos ky) 2)))
(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(pow (sin kx) 2)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (sin kx) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
(/ (* 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 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
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(- 1 (pow (cos ky) 2))
(pow (cos ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
Calls

9 calls:

TimeVariablePointExpression
18.0ms
kx
@-inf
((/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (* (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
10.0ms
kx
@inf
((/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (* (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
5.0ms
kx
@0
((/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (* (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
4.0ms
ky
@inf
((/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (* (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
4.0ms
ky
@-inf
((/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (* (cos ky) (cos ky)) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (* (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))

simplify227.0ms (2%)

Memory
-5.3MiB live, 155.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05232762
119312485
087182329
Stop Event
1×iter limit
1×node limit
Counts
80 → 78
Calls
Call 1
Inputs
1
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(+ 1 (* -1/2 (/ (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))))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (* (sin ky) (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 (cos ky) 2)))
(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(pow (sin kx) 2)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (sin kx) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
(/ (* 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 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
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(- 1 (pow (cos ky) 2))
(pow (cos ky) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (/.f64 (fma.f64 (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)) (*.f64 kx kx) #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 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (-.f64 #s(literal 2/45 binary64) (/.f64 (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)) (pow.f64 (sin.f64 ky) #s(literal 2 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))) (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 th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (*.f64 (*.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)))) (*.f64 kx kx) (sin.f64 th))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 (*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx)) (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 kx kx) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
(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 (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)) (*.f64 kx kx) #s(literal 1/2 binary64)) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (-.f64 #s(literal 2/45 binary64) (/.f64 (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)) (pow.f64 (sin.f64 ky) #s(literal 2 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))
(sqrt (- 1 (pow (cos ky) 2)))
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(fma.f64 (*.f64 (*.f64 kx kx) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (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)) (*.f64 kx kx) #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (-.f64 #s(literal 2/45 binary64) (/.f64 (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)) (pow.f64 (sin.f64 ky) #s(literal 2 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)))) (*.f64 kx kx) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (*.f64 kx kx) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))
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(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (sin.f64 th)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))) (fma.f64 (*.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (sin.f64 th)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (fma.f64 #s(literal -1/5040 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (/.f64 (*.f64 #s(literal -1/240 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (/.f64 (*.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (*.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal 1/2 binary64) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1/2 binary64)) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 ky ky)) (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 ky ky) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (*.f64 ky ky))) ky)
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(*.f64 (fma.f64 (-.f64 (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(*.f64 (fma.f64 (-.f64 (*.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (*.f64 #s(literal -1/12 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))) (+.f64 (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)))) (*.f64 ky ky) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (*.f64 ky ky)) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (*.f64 ky ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)
(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 (fma.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 (*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (*.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky) ky)
(+ 1 (* -1 (pow ky 2)))
(-.f64 #s(literal 1 binary64) (*.f64 ky ky))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 1/3 binary64) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2/45 binary64) (*.f64 ky ky) #s(literal 1/3 binary64)) (*.f64 ky ky) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(- 1 (pow (cos ky) 2))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (cos ky) 2)
(pow.f64 (cos.f64 ky) #s(literal 2 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky)) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th)))))) th)
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 (fma.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 (fma.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)
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th) (sin.f64 ky)) (*.f64 (*.f64 (*.f64 th th) (*.f64 th th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (sin.f64 ky) th) th)))))) th)

rewrite115.0ms (1%)

Memory
-8.7MiB live, 67.7MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046189
074154
1270154
02143154
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
17 → 406
Calls
Call 1
Inputs
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(sin.f64 th)
#s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
#s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx))
(-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))
(*.f64 (cos.f64 ky) (cos.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))))
(*.f64 #s(literal -1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky))))
(*.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64))
(*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal 1 binary64)))
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(*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sin.f64 ky))
(/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 1 binary64)) (sin.f64 ky))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (neg.f64 (sin.f64 ky))))
(/.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky))) #s(literal -1 binary64))
(/.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (*.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) #s(literal 1 binary64)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (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 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (pow.f64 (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 (neg.f64 (sin.f64 th)) (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky)))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) #s(literal -1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 th))) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (neg.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))
(neg.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 ky)))))
(*.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 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 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)))))
(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 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (fabs.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))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (sin.f64 ky))
(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 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (exp.f64 (log.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))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(exp.f64 (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))

eval75.0ms (0.7%)

Memory
-6.7MiB live, 72.4MiB allocated
Compiler

Compiled 12 033 to 1 843 computations (84.7% saved)

prune44.0ms (0.4%)

Memory
22.1MiB live, 61.1MiB allocated
Pruning

45 alts after pruning (42 fresh and 3 done)

PrunedKeptTotal
New38925414
Fresh71724
Picked325
Done011
Total39945444
Accuracy
100.0%
Counts
444 → 45
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.6%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
53.8%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
✓99.7%
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
42.4%
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
99.5%
(/.f64 (sin.f64 th) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sin.f64 ky)))
29.5%
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
25.5%
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
51.1%
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
51.0%
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
53.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
39.7%
(*.f64 (/.f64 (/.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))) (sin.f64 th))
29.9%
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
▶99.6%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
▶79.4%
(*.f64 (/.f64 (sin.f64 ky) (/.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))) (sin.f64 th))
79.2%
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
✓38.8%
(*.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))
32.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
32.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
13.9%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
▶37.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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))
25.2%
(*.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))
29.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
▶23.4%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
15.2%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
13.7%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
51.0%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
42.4%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
38.7%
(*.f64 (*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 ky)) (sin.f64 th))
99.5%
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
69.3%
(*.f64 (*.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
48.0%
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
48.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
47.8%
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
25.1%
(*.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))
25.5%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
93.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
17.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
16.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
45.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
23.0%
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
45.5%
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (*.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)))))))
✓30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
16.9%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
17.0%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
▶16.8%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Compiler

Compiled 2 142 to 1 624 computations (24.2% saved)

simplify0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

localize656.0ms (5.9%)

Memory
-144.8MiB live, 432.5MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.24219119935356562
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
accuracy3.375424430543204
(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))))))
accuracy12.991779367059534
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))
accuracy14.249219357035102
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
accuracy0.24219119935356562
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
accuracy3.384731532291253
(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))
accuracy12.97825191200341
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))
accuracy31.462988182134428
#s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx))
accuracy0.14453125
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy0.16796875
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
accuracy31.27391694725741
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy33.325292217149844
#s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))
accuracy0.05078125
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
accuracy0.13596623016428752
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy31.27391694725741
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy44.24692519517099
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy0.0078125
(sin.f64 ky)
accuracy0.078125
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy0.24609375
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
accuracy0.3359375
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
Samples
352.0ms78×1valid
195.0ms98×2valid
53.0ms80×0valid
Compiler

Compiled 979 to 125 computations (87.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 549.0ms
ival-cos: 343.0ms (62.5% of total)
ival-mult: 72.0ms (13.1% of total)
adjust: 33.0ms (6% of total)
ival-sin: 24.0ms (4.4% of total)
ival-div: 20.0ms (3.6% of total)
ival-hypot: 12.0ms (2.2% of total)
ival-sqrt: 10.0ms (1.8% of total)
ival-sub: 9.0ms (1.6% of total)
const: 9.0ms (1.6% of total)
ival-add: 9.0ms (1.6% of total)
ival-pow2: 4.0ms (0.7% of total)
ival-fabs: 1.0ms (0.2% of total)
exact: 1.0ms (0.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series43.0ms (0.4%)

Memory
-1.2MiB live, 75.7MiB allocated
Counts
19 → 112
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
#s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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 (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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))
(-.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 (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))))))
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
Outputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ (sin th) (sin ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(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)))))))))))))
(* 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 2) (sqrt (- 1 (cos (* -2 ky)))))
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* -2 ky))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* -2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* -2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* -2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* -2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* -2 ky))))))) (* (pow (sqrt 2) 2) (- 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 (cos ky) 2)))
(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))
(- 1 (cos (* 2 kx)))
(sqrt (+ (* 2 (- 1 (cos (* -2 ky)))) (* 2 (- 1 (cos (* 2 kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
(sin kx)
(+ (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
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
1
(+ 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)))
(* 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 2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(- 1/2 (* 1/2 (cos (* 2 ky))))
(cos (* 2 ky))
(- 1 (cos (* -2 ky)))
(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 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
(* -1/6 (pow th 2))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -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
7.0ms
kx
@-inf
((* (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (+ (* (* th th) -1/6) 1) th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* -2 ky))) (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (cos (* -2 ky)))
6.0ms
kx
@inf
((* (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (+ (* (* th th) -1/6) 1) th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* -2 ky))) (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (cos (* -2 ky)))
5.0ms
th
@inf
((* (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (+ (* (* th th) -1/6) 1) th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* -2 ky))) (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (cos (* -2 ky)))
5.0ms
ky
@inf
((* (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (+ (* (* th th) -1/6) 1) th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* -2 ky))) (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (cos (* -2 ky)))
4.0ms
ky
@-inf
((* (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin th) (+ (* (* th th) -1/6) 1) (* (+ (* (* th th) -1/6) 1) th) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (sin th)) (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)) (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (cos (* 2 ky)) (- 1 (cos (* 2 kx))) (- 1 (cos (* -2 ky))) (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (cos (* -2 ky)))

simplify188.0ms (1.7%)

Memory
21.3MiB live, 259.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06773694
124813285
095303113
Stop Event
1×iter limit
1×node limit
Counts
112 → 110
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))))))
(sqrt (- 1 (pow (cos ky) 2)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
(* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (sin ky) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))))) (sqrt (- 1 (pow (cos ky) 2))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))) (- 1 (pow (cos ky) 2)))) (+ (* 2/45 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (+ (* 2/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3))) (/ 1 (pow (- 1 (pow (cos ky) 2)) 4)))))))) (sqrt (- 1 (pow (cos ky) 2))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- 1 (pow (cos ky) 2)) 2))) (* 3/4 (/ 1 (pow (- 1 (pow (cos ky) 2)) 3)))))) (sqrt (- 1 (pow (cos ky) 2))))))))))
(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)))))))))))))
(* 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 2) (sqrt (- 1 (cos (* -2 ky)))))
(+ (* 2 (* (/ (pow kx 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* (sqrt 2) (sqrt (- 1 (cos (* -2 ky))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* -2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* -2 ky)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* -2 ky))))) (* (pow kx 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* -2 ky))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* -2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* -2 ky))))))) (* (pow (sqrt 2) 2) (- 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 (cos ky) 2)))
(* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(pow (sin kx) 2)
(sqrt (- (+ 1/2 (pow (sin kx) 2)) (* 1/2 (cos (* 2 ky)))))
(- 1 (cos (* 2 kx)))
(sqrt (+ (* 2 (- 1 (cos (* -2 ky)))) (* 2 (- 1 (cos (* 2 kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
(sin kx)
(+ (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
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
1
(+ 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)))
(* 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 2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(- 1/2 (* 1/2 (cos (* 2 ky))))
(cos (* 2 ky))
(- 1 (cos (* -2 ky)))
(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 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(+ 1 (* -1/6 (pow th 2)))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
(* -1/6 (pow th 2))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* -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 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 kx kx) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (/.f64 (sin.f64 th) (sin.f64 ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(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))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (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)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 ky)) (*.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 ky))
(sqrt (- 1 (pow (cos ky) 2)))
(sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 kx kx)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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))) (*.f64 kx kx) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+ (sqrt (- 1 (pow (cos ky) 2))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- 1 (pow (cos ky) 2))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- 1 (pow (cos ky) 2))))) (- 1 (pow (cos ky) 2)))))) (sqrt (/ 1 (- 1 (pow (cos ky) 2)))))))))))
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(sqrt (- 1/2 (* 1/2 (cos (* 2 ky)))))
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(* (sqrt 2) (sqrt (- 1 (cos (* -2 ky)))))
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(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))
(sqrt (+ (* 2 (- 1 (cos (* -2 ky)))) (* 2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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))))))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
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(/ (sin th) (sin kx))
(/.f64 (sin.f64 th) (sin.f64 kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(fma.f64 (*.f64 ky ky) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (sin.f64 th) (sin.f64 kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (*.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)) (sin.f64 kx)) (*.f64 ky ky)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
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(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal 1/2 binary64) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (*.f64 ky ky)) #s(literal 1/2 binary64)) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 kx))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 ky ky)) (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64))) (sin.f64 kx)) (*.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 kx))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 ky ky) #s(literal 1/120 binary64)) (*.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(*.f64 (fma.f64 (*.f64 (neg.f64 ky) ky) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
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(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
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(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(*.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(*.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (*.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))
1
#s(literal 1 binary64)
(+ 1 (* -2 (pow ky 2)))
(fma.f64 (*.f64 ky ky) #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow ky 2) (- (* 2/3 (pow ky 2)) 2)))
(fma.f64 (fma.f64 (*.f64 ky ky) #s(literal 2/3 binary64) #s(literal -2 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/3 (* -4/45 (pow ky 2)))) 2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -4/45 binary64) (*.f64 ky ky) #s(literal 2/3 binary64)) (*.f64 ky ky) #s(literal -2 binary64)) (*.f64 ky ky) #s(literal 1 binary64))
(* 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 (fma.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 (fma.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 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)))
(+ (* 2 (* (/ (pow ky 2) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))))
(fma.f64 (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 ky ky) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 4 binary64) #s(literal 4/3 binary64)) (*.f64 ky ky)) (sqrt.f64 #s(literal 2 binary64))) (*.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))))
(+ (* (sqrt 2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 8/45 (* -2 (/ (+ 4/3 (* 4 (/ 1 (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 2) 2) (- 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 8/45 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 4 binary64) #s(literal 4/3 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 (fma.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) #s(literal 4 binary64) #s(literal 4/3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 ky ky) (*.f64 (/.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))) #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))))
(- 1/2 (* 1/2 (cos (* 2 ky))))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))
(cos (* 2 ky))
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
(- 1 (cos (* -2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))
(cos (* -2 ky))
(cos.f64 (*.f64 #s(literal -2 binary64) 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))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 (sin.f64 ky) th)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 th (*.f64 (sin.f64 ky) th)) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (pow.f64 th #s(literal 3 binary64)) (*.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 (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 (sin.f64 ky) th)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 th (*.f64 (sin.f64 ky) th))))) (*.f64 (*.f64 th th) (*.f64 th th)))) th)
(* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th)
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(*.f64 (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 th th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) th)
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 (*.f64 th th) (*.f64 th th)))) th)
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 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 th th) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))
(*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 (sin.f64 ky) th)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (*.f64 th (*.f64 (sin.f64 ky) th)) (*.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (pow.f64 th #s(literal 3 binary64)) (*.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 (+ (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ 1 (pow (sin kx) 2)) (pow (cos ky) 2))))))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (*.f64 th (*.f64 (sin.f64 ky) th)) (sin.f64 ky)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (*.f64 #s(literal -1/5040 binary64) (*.f64 th (*.f64 (sin.f64 ky) th))))) (*.f64 (*.f64 th th) (*.f64 th th)))) th)
(* -1/6 (pow th 2))
(*.f64 (*.f64 th th) #s(literal -1/6 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))
(* -1/6 (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 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 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)))

rewrite180.0ms (1.6%)

Memory
0.6MiB live, 225.0MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
059235
097196
1387195
23527195
08048195
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
19 → 540
Calls
Call 1
Inputs
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
#s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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 (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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))
(-.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 (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))))))
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
Outputs
(*.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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 #s(literal 1 binary64) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (neg.f64 (sin.f64 th))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) (neg.f64 (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 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th))
(*.f64 (neg.f64 (sin.f64 th)) (/.f64 #s(literal 1 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) #s(literal -1 binary64))
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (neg.f64 (neg.f64 (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
(/.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)))))
(*.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 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 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)))))
(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 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (fabs.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))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (sin.f64 ky))
(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 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (exp.f64 (log.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))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
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(fma.f64 (pow.f64 (cos.f64 ky) #s(literal 1 binary64)) (pow.f64 (cos.f64 ky) #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (pow.f64 (cos.f64 ky) #s(literal 1 binary64)) (pow.f64 (cos.f64 ky) #s(literal 1 binary64)) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (pow.f64 (cos.f64 ky) #s(literal 1 binary64)) (pow.f64 (cos.f64 ky) #s(literal 1 binary64)) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (neg.f64 (cos.f64 ky))) (neg.f64 (neg.f64 (cos.f64 ky))) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (neg.f64 (neg.f64 (cos.f64 ky))) (neg.f64 (neg.f64 (cos.f64 ky))) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (neg.f64 (neg.f64 (cos.f64 ky))) (neg.f64 (neg.f64 (cos.f64 ky))) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (fabs.f64 (cos.f64 ky))) (neg.f64 (fabs.f64 (cos.f64 ky))) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (neg.f64 (fabs.f64 (cos.f64 ky))) (neg.f64 (fabs.f64 (cos.f64 ky))) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (neg.f64 (fabs.f64 (cos.f64 ky))) (neg.f64 (fabs.f64 (cos.f64 ky))) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (sin.f64 (*.f64 #s(literal 2 binary64) ky)) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (*.f64 #s(literal -2 binary64) ky)) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (*.f64 (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal -2 binary64) ky))))
(fma.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (*.f64 (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 2 binary64) ky))))
(fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (+.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (cos.f64 ky)) (neg.f64 (cos.f64 ky)) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (neg.f64 (cos.f64 ky)) (neg.f64 (cos.f64 ky)) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (neg.f64 (cos.f64 ky)) (neg.f64 (cos.f64 ky)) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (fabs.f64 (cos.f64 ky)) (fabs.f64 (cos.f64 ky)) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (fabs.f64 (cos.f64 ky)) (fabs.f64 (cos.f64 ky)) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (fabs.f64 (cos.f64 ky)) (fabs.f64 (cos.f64 ky)) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(fma.f64 (+.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (+.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 1/2 binary64) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (+.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) #s(literal 1/2 binary64) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (*.f64 (sin.f64 #s(literal 0 binary64)) (sin.f64 (*.f64 #s(literal 2 binary64) ky))))
(fma.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (*.f64 (sin.f64 #s(literal 0 binary64)) (sin.f64 (*.f64 #s(literal -2 binary64) ky))))
(fma.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (cos.f64 ky) (cos.f64 ky) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 (cos.f64 ky) (cos.f64 ky) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 (cos.f64 ky) (cos.f64 ky) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(fma.f64 (sin.f64 ky) (neg.f64 (sin.f64 ky)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(sin.f64 (+.f64 (-.f64 (neg.f64 ky) ky) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (-.f64 ky (neg.f64 ky)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) (neg.f64 ky)))
(sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 #s(literal -2 binary64) ky)))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) ky)))
(-.f64 (-.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky))))
(-.f64 (-.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64))))
(-.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(cos.f64 (+.f64 (+.f64 ky (PI.f64)) (+.f64 ky (PI.f64))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 ky (PI.f64))))
(cos.f64 (-.f64 (neg.f64 ky) ky))
(cos.f64 (-.f64 ky (neg.f64 ky)))
(cos.f64 (*.f64 #s(literal -2 binary64) ky))
(cos.f64 (*.f64 #s(literal 2 binary64) ky))
(+.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal -2 binary64) ky))))
(+.f64 (*.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (sin.f64 (*.f64 #s(literal 2 binary64) ky))))
(+.f64 (-.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 (sin.f64 #s(literal 0 binary64)) (sin.f64 (*.f64 #s(literal 2 binary64) ky))))
(+.f64 (*.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (*.f64 #s(literal -2 binary64) ky))) (*.f64 (sin.f64 #s(literal 0 binary64)) (sin.f64 (*.f64 #s(literal -2 binary64) ky))))
(+.f64 (-.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal -2 binary64) ky)) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 2 binary64) ky)) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(+.f64 (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (*.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 ky))))
(+.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (*.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 ky))))
(+.f64 (pow.f64 (cos.f64 ky) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

eval124.0ms (1.1%)

Memory
9.4MiB live, 171.8MiB allocated
Compiler

Compiled 23 092 to 3 541 computations (84.7% saved)

prune80.0ms (0.7%)

Memory
-27.2MiB live, 136.5MiB allocated
Pruning

68 alts after pruning (63 fresh and 5 done)

PrunedKeptTotal
New59434628
Fresh82937
Picked325
Done033
Total60568673
Accuracy
100.0%
Counts
673 → 68
Alt Table
Click to see full alt table
StatusAccuracyProgram
95.6%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
53.8%
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
29.2%
(/.f64 (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
✓99.7%
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
42.4%
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
99.5%
(/.f64 (sin.f64 th) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sin.f64 ky)))
29.5%
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
25.5%
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
99.5%
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
51.1%
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
51.0%
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
53.7%
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
29.2%
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
39.7%
(*.f64 (/.f64 (/.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))) (sin.f64 th))
✓99.6%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
42.4%
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
30.8%
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
29.5%
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
79.2%
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
79.4%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th))
36.8%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
27.7%
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
✓38.8%
(*.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))
32.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
37.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
46.0%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
37.3%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
14.2%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
8.6%
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (sin.f64 th))
46.3%
(*.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))
25.2%
(*.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))
29.5%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
51.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
23.4%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
10.7%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
10.4%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
15.2%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
7.7%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
37.0%
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
13.7%
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
51.0%
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
38.7%
(*.f64 (*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 ky)) (sin.f64 th))
99.5%
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
48.0%
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
23.4%
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
48.0%
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
23.4%
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
23.3%
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
25.1%
(*.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))
25.5%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
93.8%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
16.4%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
45.0%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
21.3%
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
23.0%
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
45.5%
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (*.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)))))))
✓30.9%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
17.0%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
16.8%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
16.9%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
17.0%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
✓16.8%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
16.8%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
16.8%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
8.0%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
10.5%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
5.4%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
10.5%
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
Compiler

Compiled 4 666 to 1 921 computations (58.8% saved)

regimes252.0ms (2.3%)

Memory
10.2MiB live, 410.6MiB allocated
Counts
102 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (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 kx) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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)))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (*.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) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (/.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))) (sin.f64 th))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (sin.f64 ky)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.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 ky) (sqrt.f64 (+.f64 (exp.f64 (*.f64 (log.f64 (neg.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 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (sin.f64 ky) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) (*.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64))) (sin.f64 th))
(*.f64 (*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (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))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64))))) (sin.f64 th))
Outputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
Calls

9 calls:

30.0ms
kx
29.0ms
(sin.f64 kx)
28.0ms
(sin.f64 th)
28.0ms
(*.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))
27.0ms
(sin.f64 ky)
Results
AccuracySegmentsBranch
99.7%1kx
99.7%1ky
99.7%1th
99.7%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.7%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.7%1(sin.f64 ky)
99.7%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.7%1(sin.f64 kx)
99.7%1(sin.f64 th)
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes216.0ms (1.9%)

Memory
-2.8MiB live, 268.6MiB allocated
Counts
80 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (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 kx) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
Calls

9 calls:

42.0ms
(sin.f64 ky)
23.0ms
kx
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))
22.0ms
(sin.f64 th)
21.0ms
th
Results
AccuracySegmentsBranch
99.7%1kx
99.7%1ky
99.7%1th
99.7%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.7%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.7%1(sin.f64 ky)
99.7%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.7%1(sin.f64 kx)
99.7%1(sin.f64 th)
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes204.0ms (1.8%)

Memory
4.9MiB live, 242.9MiB allocated
Counts
75 → 1
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
Outputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
Calls

9 calls:

28.0ms
(sin.f64 th)
21.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
20.0ms
th
20.0ms
(sin.f64 ky)
20.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
99.6%1ky
99.6%1(sin.f64 th)
99.6%1kx
99.6%1th
99.6%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
99.6%1(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
99.6%1(sin.f64 ky)
99.6%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
99.6%1(sin.f64 kx)
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes209.0ms (1.9%)

Memory
4.1MiB live, 278.3MiB allocated
Counts
74 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) 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))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.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)))) (sin.f64 th))
Outputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th))
Calls

9 calls:

35.0ms
(*.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))
25.0ms
(sin.f64 ky)
22.0ms
(sin.f64 th)
22.0ms
ky
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
96.1%3kx
98.9%2ky
89.7%2th
89.4%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))
99.1%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)))))
98.9%3(sin.f64 ky)
96.1%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
96.1%4(sin.f64 kx)
89.4%3(sin.f64 th)
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes186.0ms (1.7%)

Memory
8.5MiB live, 326.2MiB allocated
Counts
71 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 ky) (cos.f64 ky)))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
Calls

9 calls:

21.0ms
(sin.f64 ky)
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)))))
20.0ms
(sin.f64 th)
20.0ms
kx
19.0ms
th
Results
AccuracySegmentsBranch
75.7%4(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
79.6%5(sin.f64 th)
78.0%3th
74.5%4(sin.f64 kx)
87.3%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)))))
75.9%4(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
75.4%4kx
76.8%3(sin.f64 ky)
76.8%2ky
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes20.0ms (0.2%)

Memory
35.5MiB live, 35.5MiB allocated
Counts
69 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #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)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))
Calls

1 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)))))
Results
AccuracySegmentsBranch
87.3%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)

regimes23.0ms (0.2%)

Memory
-3.9MiB live, 33.6MiB allocated
Counts
65 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #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)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
Calls

1 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)))))
Results
AccuracySegmentsBranch
87.2%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
-3.6MiB live, 33.5MiB allocated
Counts
64 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (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 ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
Calls

1 calls:

19.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
87.2%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
-4.9MiB live, 32.3MiB allocated
Counts
62 → 6
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (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 ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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
87.1%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)

regimes66.0ms (0.6%)

Memory
-4.7MiB live, 78.5MiB allocated
Counts
61 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
Calls

3 calls:

27.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
20.0ms
th
16.0ms
ky
Results
AccuracySegmentsBranch
75.5%2th
69.8%3ky
79.1%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 15 to 17 computations (-13.3% saved)

regimes148.0ms (1.3%)

Memory
30.7MiB live, 224.9MiB allocated
Counts
60 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/315 binary64) (*.f64 kx kx) #s(literal 2/45 binary64)) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
Calls

8 calls:

24.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
20.0ms
kx
19.0ms
th
19.0ms
(sin.f64 th)
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
72.6%4(sin.f64 kx)
72.5%3kx
60.5%4(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
72.4%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
67.4%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)))))
53.8%1(sin.f64 th)
69.8%4(sin.f64 ky)
53.8%1th
Compiler

Compiled 41 to 48 computations (-17.1% saved)

regimes21.0ms (0.2%)

Memory
-3.7MiB live, 34.1MiB allocated
Counts
56 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (*.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))) (-.f64 #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 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
Calls

1 calls:

15.0ms
kx
Results
AccuracySegmentsBranch
72.4%3kx
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes21.0ms (0.2%)

Memory
-13.3MiB live, 31.8MiB allocated
Counts
55 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 ky) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (PI.f64) #s(literal 1/2 binary64) ky))))))))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (fma.f64 (cos.f64 (*.f64 #s(literal -2 binary64) ky)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
Calls

1 calls:

18.0ms
kx
Results
AccuracySegmentsBranch
72.4%3kx
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes18.0ms (0.2%)

Memory
-9.2MiB live, 29.1MiB allocated
Counts
50 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) ky)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (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))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* -2 ky)))))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -2 binary64) kx)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
Calls

1 calls:

15.0ms
kx
Results
AccuracySegmentsBranch
72.4%3kx
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes55.0ms (0.5%)

Memory
9.1MiB live, 84.9MiB allocated
Counts
48 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
Calls

4 calls:

14.0ms
ky
13.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
13.0ms
kx
13.0ms
(sin.f64 kx)
Results
AccuracySegmentsBranch
69.8%3ky
70.9%4(sin.f64 kx)
68.3%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
68.4%3kx
Compiler

Compiled 8 to 16 computations (-100% saved)

regimes114.0ms (1%)

Memory
-2.6MiB live, 115.8MiB allocated
Counts
46 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (*.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) #s(literal -1 binary64)) #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1/2 (* (cos (* 2 ky)) 1/2)))) (sqrt.f64 (-.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 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))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

6 calls:

31.0ms
(sin.f64 kx)
30.0ms
(sin.f64 ky)
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)))))
13.0ms
kx
12.0ms
ky
Results
AccuracySegmentsBranch
66.7%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
63.5%3(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
62.8%3(sin.f64 ky)
63.5%3kx
64.7%3(sin.f64 kx)
62.8%2ky
Compiler

Compiled 23 to 31 computations (-34.8% saved)

regimes12.0ms (0.1%)

Memory
21.7MiB live, 21.7MiB allocated
Counts
39 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
Outputs
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

1 calls:

10.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
66.7%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes14.0ms (0.1%)

Memory
-14.3MiB live, 23.2MiB allocated
Counts
37 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
Outputs
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

1 calls:

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
66.7%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes149.0ms (1.3%)

Memory
-23.0MiB live, 131.9MiB allocated
Counts
36 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #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))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) (sin.f64 ky))
Outputs
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

9 calls:

51.0ms
(sin.f64 ky)
26.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
10.0ms
(sin.f64 kx)
10.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
10.0ms
kx
Results
AccuracySegmentsBranch
43.2%2th
43.2%3(sin.f64 th)
44.1%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))
51.6%3(sin.f64 ky)
44.8%2kx
43.9%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
44.9%2ky
46.0%3(sin.f64 kx)
56.8%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes28.0ms (0.2%)

Memory
-27.1MiB live, 11.8MiB allocated
Counts
33 → 3
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(*.f64 (/.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #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 th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (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(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky))) (*.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 (*.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(approx (cos (* 2 ky)) #s(literal 1 binary64)) #s(literal 1/2 binary64)))))) (sin.f64 th))
Outputs
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

1 calls:

26.0ms
(/.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
56.0%3(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes14.0ms (0.1%)

Memory
20.8MiB live, 20.8MiB allocated
Counts
21 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
Outputs
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

2 calls:

6.0ms
(sin.f64 ky)
6.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
44.7%2(sin.f64 ky)
49.1%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 15 to 15 computations (0% saved)

regimes7.0ms (0.1%)

Memory
9.5MiB live, 9.5MiB allocated
Counts
19 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (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))
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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

1 calls:

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
49.1%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes16.0ms (0.1%)

Memory
-35.1MiB live, 8.8MiB allocated
Counts
18 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
Outputs
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
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
47.3%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes47.0ms (0.4%)

Memory
7.0MiB live, 80.0MiB allocated
Counts
17 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky))))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
Outputs
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

8 calls:

8.0ms
(sin.f64 ky)
8.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
5.0ms
ky
5.0ms
(sin.f64 kx)
5.0ms
kx
Results
AccuracySegmentsBranch
38.5%3(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
33.6%2th
35.7%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
35.8%3(sin.f64 kx)
37.5%2(sin.f64 ky)
35.4%2kx
37.6%2ky
42.1%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 40 to 47 computations (-17.5% saved)

regimes21.0ms (0.2%)

Memory
4.8MiB live, 43.2MiB allocated
Counts
15 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (pow.f64 th #s(literal 3 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(literal 1 binary64)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64))))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))
Calls

4 calls:

6.0ms
(sin.f64 ky)
5.0ms
(sin.f64 th)
5.0ms
ky
4.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
34.0%2(sin.f64 ky)
33.6%2ky
34.2%3(sin.f64 th)
37.1%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 18 to 22 computations (-22.2% saved)

regimes30.0ms (0.3%)

Memory
7.7MiB live, 53.8MiB allocated
Counts
8 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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 (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.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)))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
Calls

9 calls:

6.0ms
(sin.f64 ky)
3.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
3.0ms
(sin.f64 kx)
3.0ms
th
3.0ms
ky
Results
AccuracySegmentsBranch
19.4%2(sin.f64 th)
19.3%2th
20.3%2ky
20.6%2(sin.f64 ky)
19.5%2(sin.f64 kx)
20.5%2kx
20.5%2(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
24.1%2(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
23.5%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes5.0ms (0%)

Memory
11.8MiB live, 11.8MiB allocated
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 th th))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (fma.f64 th #s(literal 1 binary64) (*.f64 th (*.f64 #s(literal -1/6 binary64) (*.f64 th th))))))
Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
Calls

2 calls:

2.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
2.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
Results
AccuracySegmentsBranch
23.3%2(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
23.3%2(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 29 to 24 computations (17.2% saved)

regimes13.0ms (0.1%)

Memory
-10.2MiB live, 28.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

9 calls:

3.0ms
(sin.f64 ky)
1.0ms
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
1.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
1.0ms
(sin.f64 kx)
1.0ms
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
Results
AccuracySegmentsBranch
10.5%1th
10.5%1(sin.f64 th)
10.5%1(sin.f64 kx)
10.5%1ky
10.5%1kx
10.5%1(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
10.5%1(sin.f64 ky)
10.5%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)))))
10.5%1(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch32.0ms (0.3%)

Memory
-7.9MiB live, 30.1MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
30.0ms
6.308054972260424e-5
0.7963696430129814
Samples
16.0ms128×0valid
Compiler

Compiled 371 to 322 computations (13.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sin: 7.0ms (57.3% of total)
ival-pow2: 2.0ms (16.4% of total)
ival-div: 1.0ms (8.2% of total)
ival-add: 1.0ms (8.2% of total)
ival-mult: 1.0ms (8.2% of total)
ival-sqrt: 1.0ms (8.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory
2.3MiB live, 2.3MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.0000056165380304
0.0ms
0.9947818255290916
0.9999999996094946
0.0ms
0.017560687712785333
0.02040622816525496
0.0ms
-0.4424933047277975
-0.4055373724054084
0.0ms
-0.9999999999998572
-0.9999846708835508
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.3MiB live, 2.3MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.0000056165380304
0.0ms
0.9947818255290916
0.9999999996094946
0.0ms
0.017560687712785333
0.02040622816525496
0.0ms
-0.4424933047277975
-0.4055373724054084
0.0ms
-0.9999999999998572
-0.9999846708835508
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.6MiB live, 2.6MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.0000056165380304
0.0ms
0.9947818255290916
0.9999999996094946
0.0ms
0.017560687712785333
0.02040622816525496
0.0ms
-0.4424933047277975
-0.4055373724054084
0.0ms
-0.9999999999998572
-0.9999846708835508
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
3.0MiB live, 3.0MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.0000056165380304
0.0ms
0.9947818255290916
0.9999999996094946
0.0ms
0.017560687712785333
0.02040622816525496
0.0ms
-0.4424933047277975
-0.4055373724054084
0.0ms
-0.9999999999998572
-0.9999846708835508
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.9MiB live, 2.9MiB allocated
Algorithm
5×left-value
Steps
TimeLeftRight
0.0ms
1.0
1.0000056165380304
0.0ms
0.9947818255290916
0.9999999996094946
0.0ms
0.017560687712785333
0.02040622816525496
0.0ms
-0.4424933047277975
-0.4055373724054084
0.0ms
-0.9999999999998572
-0.9999846708835508
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch6.0ms (0.1%)

Memory
12.9MiB live, 12.9MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
5.0ms
0.003501907321463618
0.0038629070480589727
Samples
4.0ms32×0valid
Compiler

Compiled 133 to 108 computations (18.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-sin: 2.0ms (65.6% of total)
ival-pow2: 1.0ms (32.8% of total)
ival-div: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch61.0ms (0.5%)

Memory
-9.0MiB live, 69.4MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
37.0ms
1.4302545395725468
459.1644205785658
20.0ms
2.615593859689757e-160
1.6123248050070914e-158
Samples
46.0ms240×0valid
Compiler

Compiled 1 091 to 842 computations (22.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-sin: 16.0ms (59.1% of total)
ival-pow2: 4.0ms (14.8% of total)
ival-add: 2.0ms (7.4% of total)
ival-mult: 2.0ms (7.4% of total)
ival-sqrt: 2.0ms (7.4% of total)
ival-div: 1.0ms (3.7% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch4.0ms (0%)

Memory
5.5MiB live, 5.5MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
2.0ms
1.4302545395725468
459.1644205785658
1.0ms
2.615593859689757e-160
1.6123248050070914e-158
Compiler

Compiled 1 016 to 812 computations (20.1% saved)

bsearch4.0ms (0%)

Memory
5.4MiB live, 5.4MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
2.0ms
1.4302545395725468
459.1644205785658
1.0ms
2.615593859689757e-160
1.6123248050070914e-158
Compiler

Compiled 926 to 797 computations (13.9% saved)

bsearch8.0ms (0.1%)

Memory
-33.5MiB live, 4.7MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
1.0ms
1.4302545395725468
459.1644205785658
1.0ms
2.615593859689757e-160
1.6123248050070914e-158
Compiler

Compiled 836 to 722 computations (13.6% saved)

bsearch36.0ms (0.3%)

Memory
9.6MiB live, 82.2MiB allocated
Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
19.0ms
6.68643752985706e-6
6.308054972260424e-5
13.0ms
4.182041724490711e-151
8.619653027045804e-151
Samples
24.0ms176×0valid
Compiler

Compiled 536 to 443 computations (17.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-sin: 9.0ms (46.1% of total)
ival-mult: 4.0ms (20.5% of total)
ival-pow2: 3.0ms (15.4% of total)
ival-div: 1.0ms (5.1% of total)
ival-add: 1.0ms (5.1% of total)
ival-sqrt: 1.0ms (5.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory
3.9MiB live, 4.0MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.06617082064637783
0.08135170823240392
0.0ms
-0.6256486761383357
-0.6040208933458397
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
3.0MiB live, 3.0MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.06617082064637783
0.08135170823240392
0.0ms
-0.6256486761383357
-0.6040208933458397
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.7MiB live, 2.7MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.06617082064637783
0.08135170823240392
0.0ms
-0.6256486761383357
-0.6040208933458397
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
2.2MiB live, 2.1MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.06617082064637783
0.08135170823240392
0.0ms
-0.7531663410179831
-0.7461281551833583
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
2×left-value
Steps
TimeLeftRight
0.0ms
0.017560687712785333
0.02040622816525496
0.0ms
-0.18759739663657032
7.704284665472173e-307
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.017560687712785333
0.02040622816525496
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.017560687712785333
0.02040622816525496
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
0.017560687712785333
0.02040622816525496
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
1.102477698214602e-17
5.943392260076405e-13
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch23.0ms (0.2%)

Memory
-23.1MiB live, 26.0MiB allocated
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.4034376290496256e-36
3.3529978876715754e-26
Samples
9.0ms160×0valid
Compiler

Compiled 599 to 419 computations (30.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-sin: 4.0ms (81.4% of total)
ival-mult: 1.0ms (20.4% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
8.394007e-318
1.9789997331250437e-307
Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
8.394007e-318
1.9789997331250437e-307
Compiler

Compiled 19 to 19 computations (0% saved)

simplify58.0ms (0.5%)

Memory
12.1MiB live, 88.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02792795
13462795
23782795
34262795
45272795
56092795
66552795
76942795
87002795
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(if (<=.f64 ky #s(literal 7378697629483821/4611686018427387904 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (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 -5584463537939415/9007199254740992 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (fabs.f64 (sin.f64 ky)))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/72057594037927936 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -5584463537939415/9007199254740992 binary64)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (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 5764607523034235/72057594037927936 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3/4 binary64)) (*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (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 5764607523034235/72057594037927936 binary64)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) (*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 th th) #s(literal 1 binary64)) th)) #s(approx (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky))))) (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 5764607523034235/288230376151711744 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/288230376151711744 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/288230376151711744 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5764607523034235/288230376151711744 binary64)) #s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 6490371073168535/324518553658426726783156020576256 binary64)) (*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (- 1 (* (cos ky) (cos ky)))))) (/.f64 ky (sin.f64 kx))) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8420761386965163/2854495385411919762116571938898990272765493248 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (sin.f64 th)))
(if (<=.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 2024023/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th))))
(if (<=.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 2024023/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th))) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))
Outputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(if (<=.f64 ky #s(literal 7378697629483821/4611686018427387904 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.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 2 binary64))) (sin.f64 th)))
(if (<=.f64 ky #s(literal 7378697629483821/4611686018427387904 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))) (*.f64 (/.f64 (sin.f64 ky) (/.f64 (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))) #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 -9007109182748445/9007199254740992 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 -7566047373982433/18014398509481984 binary64)) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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 5764607523034235/288230376151711744 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #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 8962163258467287/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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))) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) 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 -9007109182748445/9007199254740992 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 -7566047373982433/18014398509481984 binary64)) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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 5764607523034235/288230376151711744 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #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 8962163258467287/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (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)) #s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (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))) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)))))))))
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#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(approx (sin th) (*.f64 #s(approx (+ (* (* th th) -1/6) 1) (*.f64 (*.f64 th th) #s(literal -1/6 binary64))) th)))

soundness2.0s (18.4%)

Memory
53.5MiB live, 1 620.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06773694
124813285
095303113
04512170
116121993
274091920
082891779
041184
070130
1279130
22613130
08243129
046189
074154
1270154
02143154
0208700
1710685
23162660
08290608
059235
097196
1387195
23527195
08048195
01031
01731
15531
234131
3356931
0822921
05232762
119312485
087182329
Stop Event
1×fuel
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
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 6 484 to 2 703 computations (58.3% saved)

preprocess256.0ms (2.3%)

Memory
14.7MiB live, 365.3MiB allocated
Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 5 754 to 700 computations (87.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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