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

analyze180.0ms (5.1%)

Memory

27.0MiB live, 216.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.8s (51.4%)

Memory

-3.8MiB live, 2 012.1MiB allocated

Samples

1.5s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1000.0ms

ival-sin: 558.0ms (55.8% of total)

ival-pow2: 159.0ms (15.9% of total)

ival-sqrt: 81.0ms (8.1% of total)

ival-mult: 77.0ms (7.7% of total)

ival-div: 75.0ms (7.5% of total)

ival-add: 41.0ms (4.1% of total)

ival-true: 6.0ms (0.6% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

preprocess75.0ms (2.1%)

Memory

-15.7MiB live, 61.3MiB allocated

Algorithm

2×	egg-herbie

Rules

390×	`unsub-neg`
362×	`times-frac`
340×	`associate-l`
330×	`associate-r`
282×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	166
1	104	163
2	212	163
3	384	163
4	831	163
5	1947	163
6	2502	163
7	2779	163
8	2891	163
9	2941	163
10	2956	163
11	2956	163
0	13	16
1	19	16
2	23	16
3	24	16
0	24	11

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

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

Call 2

Inputs
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(* (/ (sin ky) (sqrt (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))) (sin th))
(* (/ (sin (neg ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))) (sin th))
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin (neg th)))
(neg (* (/ (sin ky) (sqrt (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))) (sin th)))
(neg (* (/ (sin (neg ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))) (sin th)))
(neg (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin (neg th))))
(* (/ (sin kx) (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin th))
(* (/ (sin ky) (sqrt (+ (pow (sin th) 2) (pow (sin ky) 2)))) (sin kx))
(* (/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin th) 2)))) (sin ky))

Outputs
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ (sin ky) (sqrt (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))) (sin th))
(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ (sin (neg ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))) (sin th))
(/ (* (sin ky) (neg (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin (neg th)))
(/ (* (sin ky) (neg (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(neg (* (/ (sin ky) (sqrt (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))) (sin th)))
(/ (* (sin ky) (neg (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(neg (* (/ (sin (neg ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))) (sin th)))
(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(neg (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin (neg th))))
(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ (sin kx) (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin th))
(/ (* (sin kx) (sin th)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ (sin ky) (sqrt (+ (pow (sin th) 2) (pow (sin ky) 2)))) (sin kx))
(/ (* (sin ky) (sin kx)) (sqrt (+ (pow (sin ky) 2) (pow (sin th) 2))))
(* (/ (sin th) (sqrt (+ (pow (sin kx) 2) (pow (sin th) 2)))) (sin ky))
(/ (* (sin ky) (sin th)) (sqrt (+ (pow (sin kx) 2) (pow (sin th) 2))))

Symmetry

(abs kx)

(negabs ky)

(negabs th)

explain182.0ms (5.2%)

Memory

21.1MiB live, 298.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
19	-	1	(5.6789757420072856e-229 3.198827289591751e-159 3.398566838858208e-15)	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	-	0	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	0	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	0	-	`(sin.f64 kx)`
0	-	0	-	`(sin.f64 th)`
0	-	0	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	-	0	-	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
0	-	0	-	`th`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
0	-	0	-	`(sin.f64 ky)`
0	-	0	-	`ky`
0	-	0	-	`kx`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	uflow-rescue	18	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	66
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	60
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	18

Confusion

	Predicted +	Predicted -
+	18	1
-	0	237

Precision

1.0

Recall

0.9473684210526315

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	18	0	1
-	0	0	237

Precision?

1.0

Recall?

0.9473684210526315

Freqs

test

number	freq
0	238
1	18

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

77.0ms

512×

valid

Compiler

Compiled 174 to 56 computations (67.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-sin: 34.0ms (59.2% of total)

ival-pow2: 9.0ms (15.7% of total)

ival-sqrt: 5.0ms (8.7% of total)

ival-div: 3.0ms (5.2% of total)

ival-mult: 3.0ms (5.2% of total)

ival-add: 2.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	92.7%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify6.0ms (0.2%)

Memory

-32.7MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓	cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	cost-diff	7296	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Rules

16×	`-lowering-.f32`
16×	`-lowering-.f64`
6×	`*-commutative`
6×	`sin-lowering-sin.f64`
6×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	19	66
2	23	66
3	24	66
0	24	51

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sin ky)
ky
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(pow (sin kx) 2)
(sin kx)
kx
2
(pow (sin ky) 2)
(sin th)
th

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

localize56.0ms (1.6%)

Memory

26.3MiB live, 74.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	accuracy	99.6%	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
✓	accuracy	99.6%	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓	accuracy	93.1%	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Samples

36.0ms

256×

valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-sin: 16.0ms (60.4% of total)

ival-pow2: 5.0ms (18.9% of total)

ival-sqrt: 2.0ms (7.6% of total)

ival-div: 1.0ms (3.8% of total)

ival-add: 1.0ms (3.8% of total)

ival-mult: 1.0ms (3.8% of total)

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.8%)

Memory

-2.3MiB live, 36.2MiB allocated

Counts

6 → 120

Calls

Call 1

Inputs
#<alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))>
#<alt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))>
#<alt (sin ky)>
#<alt (pow (sin ky) 2)>
#<alt (pow (sin kx) 2)>

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

Calls

30 calls:

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

rewrite338.0ms (9.6%)

Memory

20.3MiB live, 522.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 346×	`accelerator-lowering-fma.f32`
4 346×	`accelerator-lowering-fma.f64`
3 626×	`-lowering-.f32`
3 626×	`-lowering-.f64`
2 248×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	53	49
2	329	49
3	2893	49
0	8275	34

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 294

Calls

Call 1

Inputs
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sin ky)
(pow (sin ky) 2)
(pow (sin kx) 2)

Outputs
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 0 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1/4 binary64) (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1/4 binary64))))
(exp.f64 (neg.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal -1/2 binary64))))
(exp.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 0 binary64)) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 0 binary64)))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (-.f64 #s(literal 0 binary64) (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(hypot.f64 (-.f64 #s(literal 0 binary64) (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (-.f64 #s(literal 0 binary64) (sin.f64 ky)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 ky)))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (sin.f64 kx))
(hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))
(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))
(/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (pow.f64 (sin.f64 ky) #s(literal 8 binary64)))) (sqrt.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (+.f64 (pow.f64 (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 18 binary64)) (pow.f64 (sin.f64 ky) #s(literal 18 binary64)))) (sqrt.f64 (.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 12 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 12 binary64)) (pow.f64 (.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 6 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 12 binary64)) (pow.f64 (sin.f64 ky) #s(literal 12 binary64)))) (sqrt.f64 (.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 12 binary64)) (pow.f64 (sin.f64 ky) #s(literal 12 binary64)))) (sqrt.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 8 binary64)) (pow.f64 (*.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) (-.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))))
(/.f64 (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 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))))))
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(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (sin.f64 ky)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (sqrt.f64 (sin.f64 ky))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 ky))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (+.f64 ky ky)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))))
(*.f64 (sin.f64 ky) (sin.f64 ky))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 ky)) (-.f64 #s(literal 0 binary64) (sin.f64 ky)))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (sin.f64 ky)) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 kx))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 kx))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (+.f64 kx kx)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 kx))))
(*.f64 (sin.f64 kx) (sin.f64 kx))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)))
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 kx)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 kx)))

simplify562.0ms (16%)

Memory

6.5MiB live, 760.8MiB allocated

Algorithm

1×	egg-herbie

Rules

14 278×	`accelerator-lowering-fma.f32`
14 278×	`accelerator-lowering-fma.f64`
6 260×	`-lowering-.f32`
6 260×	`-lowering-.f64`
5 352×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	2263
1	1011	2214
2	3860	2122
3	7803	2122
0	8106	1974

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval61.0ms (1.7%)

Memory: -8.7MiB live, 106.3MiB allocated
Compiler: Compiled 12 830 to 1 677 computations (86.9% saved)

prune119.0ms (3.4%)

Memory

21.3MiB live, 136.0MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	423	27	450
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	424	27	451

Accuracy

100.0%

Counts

451 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	26.5%	(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
	76.0%	(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))))
	26.2%	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
	76.1%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) (sin.f64 ky)))
	75.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
	26.1%	(.f64 (fma.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 th))
	76.1%	(.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky))
	29.0%	(.f64 (/.f64 (sin.f64 ky) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))) (sin.f64 th))
	78.2%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))) (sin.f64 th))
▶	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	41.5%	(.f64 (/.f64 (sin.f64 ky) (/.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 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))) (sin.f64 th))
	76.0%	(.f64 (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))) (sin.f64 th))
	76.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 th))
	42.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 (.f64 ky ky) (fma.f64 ky (*.f64 ky #s(literal 2/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64)) ky) ky)))) (sin.f64 th))
	42.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 ky ky)))) (sin.f64 th))
▶	54.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	30.8%	(*.f64 (/.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
	27.8%	(*.f64 (/.f64 ky (sin.f64 kx)) (sin.f64 th))
	76.0%	(.f64 (.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal -1/4 binary64))) (sin.f64 th))
	76.1%	(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky)) (sin.f64 th))
	50.5%	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))))) (sin.f64 th))
	92.4%	(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (sin.f64 th))
▶	76.0%	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))
▶	46.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) th))
	48.1%	(.f64 th (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
	20.8%	(.f64 ky (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)) (/.f64 (.f64 (.f64 ky ky) (*.f64 #s(literal -1/2 binary64) (sin.f64 th))) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))
▶	32.9%	(sin.f64 th)

Compiler

Compiled 1 234 to 844 computations (31.6% saved)

simplify95.0ms (2.7%)

Memory

-1.3MiB live, 117.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
✓	cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) th))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))))
✓	cost-diff	192	(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))
✓	cost-diff	192	(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))))
✓	cost-diff	384	(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))))
✓	cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓	cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	cost-diff	128	(+.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
✓	cost-diff	1024	(sqrt.f64 (+.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	cost-diff	0	(sin.f64 th)
✓	cost-diff	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	cost-diff	0	(sin.f64 ky)
✓	cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Rules

1 496×	`accelerator-lowering-fma.f32`
1 496×	`accelerator-lowering-fma.f64`
558×	`-lowering-.f32`
558×	`-lowering-.f64`
412×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	311
1	68	311
2	107	303
3	150	295
4	199	295
5	262	295
6	369	295
7	525	295
8	738	289
9	1040	289
10	1565	289
11	1890	289
12	2006	289
13	2016	289
14	2024	289
15	2030	289
0	2030	256

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th))
(/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
(sin ky)
ky
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
(sin kx)
kx
(sin th)
th
(sin th)
th
(* (/ (sin ky) (sqrt (+ (* kx kx) (pow (sin ky) 2)))) (sin th))
(/ (sin ky) (sqrt (+ (* kx kx) (pow (sin ky) 2))))
(sin ky)
ky
(sqrt (+ (* kx kx) (pow (sin ky) 2)))
(+ (* kx kx) (pow (sin ky) 2))
(* kx kx)
kx
(pow (sin ky) 2)
2
(sin th)
th
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx))))))))
(* (sin ky) (sin th))
(sin ky)
ky
(sin th)
th
(sqrt (/ 1 (+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx)))))))
(/ 1 (+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx))))))
1
(+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx)))))
(- 1 (cos (+ ky ky)))
(cos (+ ky ky))
(+ ky ky)
1/2
(+ 1/2 (* -1/2 (cos (+ kx kx))))
(* -1/2 (cos (+ kx kx)))
-1/2
(cos (+ kx kx))
(+ kx kx)
kx
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin ky) th))
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
1
(+ (pow (sin ky) 2) (pow (sin kx) 2))
(pow (sin ky) 2)
(sin ky)
ky
2
(pow (sin kx) 2)
(sin kx)
kx
(* (sin ky) th)
th

Outputs
(* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin ky)
(sin.f64 ky)
ky
(sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin kx)
(sin.f64 kx)
kx
(sin th)
(sin.f64 th)
th
(sin th)
(sin.f64 th)
th
(* (/ (sin ky) (sqrt (+ (* kx kx) (pow (sin ky) 2)))) (sin th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) kx))
(/ (sin ky) (sqrt (+ (* kx kx) (pow (sin ky) 2))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) kx))
(sin ky)
(sin.f64 ky)
ky
(sqrt (+ (* kx kx) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 ky) kx)
(+ (* kx kx) (pow (sin ky) 2))
(fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(* kx kx)
(*.f64 kx kx)
kx
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sin th)
(sin.f64 th)
th
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx))))))))
(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx)))))))
(* (sin ky) (sin th))
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin ky)
(sin.f64 ky)
ky
(sin th)
(sin.f64 th)
th
(sqrt (/ 1 (+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx)))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx))))))
(/ 1 (+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx))))))
(/.f64 #s(literal 2 binary64) (-.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx)))))
1
#s(literal 1 binary64)
(+ (* (- 1 (cos (+ ky ky))) 1/2) (+ 1/2 (* -1/2 (cos (+ kx kx)))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 ky ky)) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))
(- 1 (cos (+ ky ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
(cos (+ ky ky))
(cos.f64 (+.f64 ky ky))
(+ ky ky)
(+.f64 ky ky)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 (cos (+ kx kx))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))
(* -1/2 (cos (+ kx kx)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 0 binary64))
-1/2
#s(literal -1/2 binary64)
(cos (+ kx kx))
(cos.f64 (+.f64 kx kx))
(+ kx kx)
(+.f64 kx kx)
kx
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin ky) th))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) th))
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
1
#s(literal 1 binary64)
(+ (pow (sin ky) 2) (pow (sin kx) 2))
(+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin ky)
(sin.f64 ky)
ky
2
#s(literal 2 binary64)
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin kx)
(sin.f64 kx)
kx
(* (sin ky) th)
(*.f64 (sin.f64 ky) th)
th

localize1.0ms (0%)

Memory: 1.3MiB live, 1.3MiB allocated
Compiler: Compiled 294 to 40 computations (86.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze180.0ms (5.1%)

sample1.8s (51.4%)

preprocess75.0ms (2.1%)

explain182.0ms (5.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.2%)

localize56.0ms (1.6%)

series28.0ms (0.8%)

rewrite338.0ms (9.6%)

simplify562.0ms (16%)

eval61.0ms (1.7%)

prune119.0ms (3.4%)

simplify95.0ms (2.7%)

localize1.0ms (0%)

end0.0ms (0%)

Profiling