Metrics for Toniolo and Linder, Equation (3a)

analyze146.0ms (2.7%)

Memory

15.6MiB live, 202.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
50%	49.9%	49.9%	0.2%	0%	0%	0%	3
50%	49.9%	49.9%	0.2%	0%	0%	0%	4
50%	49.9%	49.9%	0.2%	0%	0%	0%	5
50%	49.9%	49.9%	0.2%	0%	0%	0%	6
75%	74.9%	25%	0.2%	0%	0%	0%	7
75%	74.9%	25%	0.2%	0%	0%	0%	8
75%	74.9%	25%	0.2%	0%	0%	0%	9
75%	74.9%	25%	0.2%	0%	0%	0%	10
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	11
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	12

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample2.2s (40.6%)

Memory

7.2MiB live, 2 618.7MiB allocated

Samples

1.8s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-sin: 570.0ms (36.9% of total)

ival-pow2: 278.0ms (18% of total)

ival-add: 195.0ms (12.6% of total)

ival-div: 186.0ms (12% of total)

ival-mult: 173.0ms (11.2% of total)

ival-sqrt: 129.0ms (8.3% of total)

exact: 7.0ms (0.5% of total)

ival-true: 6.0ms (0.4% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

preprocess298.0ms (5.5%)

Memory

8.2MiB live, 290.9MiB allocated

Algorithm

2×	egg-herbie

Rules

5 280×	`-lowering-.f32`
5 280×	`-lowering-.f64`
3 044×	`/-lowering-/.f32`
3 044×	`/-lowering-/.f64`
2 794×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	134	413
1	345	379
2	894	379
3	3895	379
4	7955	379
0	23	27
1	48	25
2	105	25
3	426	25
4	1730	25
5	3054	25
6	3578	25
7	3814	25
8	4322	25
9	5682	25
10	6674	25
0	10109	24

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

Outputs

(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (/.f64 (*.f64 l (*.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))

Call 2

Inputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 (neg l)) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) (neg Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 (neg l)) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) (neg Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2))))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2))))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 Om) l) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 kx) Om) 2) (+ (pow (sin l) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 ky) Om) 2) (+ (pow (sin kx) 2) (pow (sin l) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) kx) 2) (+ (pow (sin Om) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) ky) 2) (+ (pow (sin kx) 2) (pow (sin Om) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin ky) 2) (pow (sin kx) 2)))))))))

Outputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 (neg l)) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) (neg Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 (neg l)) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) (neg Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin (neg kx)) 2) (pow (sin ky) 2))))))))))
(neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(neg (sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin (neg ky)) 2))))))))))
(neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 Om) l) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow (* 2 (/ Om l)) 2)))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 kx) Om) 2) (+ (pow (sin l) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* 2 (/ kx Om)) 2) (+ (pow (sin ky) 2) (pow (sin l) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 ky) Om) 2) (+ (pow (sin kx) 2) (pow (sin l) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* 2 (/ ky Om)) 2) (+ (pow (sin kx) 2) (pow (sin l) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) kx) 2) (+ (pow (sin Om) 2) (pow (sin ky) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (/ (* 2 l) kx) 2) (+ (pow (sin ky) 2) (pow (sin Om) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) ky) 2) (+ (pow (sin kx) 2) (pow (sin Om) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (/ (* 2 l) ky) 2) (+ (pow (sin kx) 2) (pow (sin Om) 2))))))))
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin ky) 2) (pow (sin kx) 2)))))))))
(sqrt (+ 1/2 (/ 1/2 (sqrt (+ 1 (* (pow (* l (/ 2 Om)) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))

Symmetry

(abs l)

(abs Om)

(abs kx)

(abs ky)

(sort kx ky)

explain366.0ms (6.8%)

Memory

-3.4MiB live, 659.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
35	-	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))`
13	-	-	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
4	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))`
0	-	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	-	`Om`
0	-	-	`(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	-	-	`(*.f64 #s(literal 2 binary64) l)`
0	-	-	`(sin.f64 ky)`
0	-	-	`(/.f64 (*.f64 #s(literal 2 binary64) l) Om)`
0	-	-	`kx`
0	-	-	`ky`
0	-	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))`
0	-	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
0	-	-	`(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))`
0	-	-	`(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
0	-	-	`(sin.f64 kx)`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))`
0	-	-	`l`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))`	oflow-rescue	35	0
↳	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))`	overflow	29
↳	`(/.f64 (*.f64 #s(literal 2 binary64) l) Om)`	overflow	34
↳	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	overflow	64
↳	`(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`	overflow	64
↳	`(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))`	overflow	74
`*.f64`	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	*no**	8	0

Confusion

	Predicted +	Predicted -
+	2	3
-	41	210

Precision

0.046511627906976744

Recall

0.4

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	3
-	41	0	210

Precision?

0.046511627906976744

Recall?

0.4

Freqs

test

number	freq
0	213
1	43

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

98.0ms

512×

valid

Compiler

Compiled 478 to 92 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-sin: 22.0ms (30.5% of total)

ival-pow2: 17.0ms (23.6% of total)

ival-div: 10.0ms (13.9% of total)

ival-mult: 9.0ms (12.5% of total)

ival-sqrt: 7.0ms (9.7% of total)

ival-add: 6.0ms (8.3% of total)

exact: 1.0ms (1.4% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 4 to 4 computations (0% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Status

Accuracy

Program

▶

98.3%

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Compiler

Compiled 33 to 22 computations (33.3% saved)

simplify225.0ms (4.2%)

Memory

-7.1MiB live, 269.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
✓	cost-diff	5824	(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))

Rules

5 280×	`-lowering-.f32`
5 280×	`-lowering-.f64`
3 044×	`/-lowering-/.f32`
3 044×	`/-lowering-/.f64`
2 794×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	198
1	48	194
2	105	194
3	426	194
4	1730	194
5	3054	194
6	3578	194
7	3814	194
8	4322	194
9	5682	194
10	6674	194
0	10109	188

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(/ 1 2)
1
2
(+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (/ (* 2 l) Om) 2)
(/ (* 2 l) Om)
(* 2 l)
l
Om
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(pow (sin kx) 2)
(sin kx)
kx
(pow (sin ky) 2)
(sin ky)
ky

Outputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))))
(/ 1 2)
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)
(+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))))
(/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt.f64 (fma.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64)))
(+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(fma.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(.f64 (/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (.f64 Om Om)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow (/ (* 2 l) Om) 2)
(/.f64 (.f64 l (.f64 l #s(literal 4 binary64))) (*.f64 Om Om))
(/ (* 2 l) Om)
(/.f64 (*.f64 #s(literal 2 binary64) l) Om)
(* 2 l)
(*.f64 #s(literal 2 binary64) l)
l
Om
(+ (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
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin ky)
(sin.f64 ky)
ky

localize77.0ms (1.4%)

Memory

34.2MiB live, 111.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
✓	accuracy	95.1%	(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
✓	accuracy	87.3%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))

Samples

47.0ms

256×

valid

Compiler

Compiled 206 to 24 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-sin: 11.0ms (32.1% of total)

ival-pow2: 7.0ms (20.4% of total)

ival-div: 5.0ms (14.6% of total)

ival-mult: 5.0ms (14.6% of total)

ival-add: 3.0ms (8.8% of total)

ival-sqrt: 3.0ms (8.8% of total)

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

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

exact: 0.0ms (0% of total)

series76.0ms (1.4%)

Memory

-26.4MiB live, 79.6MiB allocated

Counts

8 → 276

Calls

Call 1

Inputs
#<alt (pow (/ (* 2 l) Om) 2)>
#<alt (/ 1 2)>
#<alt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))>
#<alt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))>
#<alt (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))>
#<alt (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))>
#<alt (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))>
#<alt (pow (sin ky) 2)>

Outputs
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt (* 4 (/ (pow l 2) (pow Om 2)))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* (pow l 2) (+ (* -1 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* -1/4 (* (pow l 2) (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))))))))>
#<alt (+ 1 (* (pow l 2) (+ (* -1 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow l 2) (+ (* -1/4 (* (pow l 2) (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* 64 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3) (pow Om 6)))))) (* -1/4 (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))>
#<alt (+ 1/2 (+ (* -1/32 (* (/ (pow Om 3) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))>
#<alt (+ 1/2 (+ (* -1/2 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 5))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/32 (* (/ (pow Om 3) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) l)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/32 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) l)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))>
#<alt (+ 1/2 (* Om (+ (* -1/32 (* (/ (pow Om 2) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))>
#<alt (+ 1/2 (* Om (+ (* 1/4 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/32 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 3/512 (* (/ (pow Om 2) (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5))))))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))>
#<alt (+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/4 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))>
#<alt (+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/4 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))>
#<alt (+ (* -1 (* (/ (* (pow kx 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))))>
#<alt (+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))) (* (pow kx 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* -1/4 (* (* (pow kx 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))>
#<alt (+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))) (* (pow kx 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* (pow kx 2) (+ (* -1/4 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (* -1/4 (* (* (pow kx 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))>
#<alt (+ (* -1 (* (/ (* (pow ky 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))))>
#<alt (+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))) (* (pow ky 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* -1/4 (* (* (pow ky 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))>
#<alt (+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))) (* (pow ky 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* (pow ky 2) (+ (* -1/4 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (* -1/4 (* (* (pow ky 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))>
#<alt 1>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))>
#<alt (* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))>
#<alt (* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))>
#<alt (* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))>
#<alt (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))>
#<alt (* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))>
#<alt (* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))>
#<alt (* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))>
#<alt (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))>
#<alt (/ (+ (* 4 (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (pow Om 2)) (pow Om 2))>
#<alt (/ (+ (* 4 (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (pow Om 2)) (pow Om 2))>
#<alt (/ (+ (* 4 (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (pow Om 2)) (pow Om 2))>
#<alt 1>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt 1>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))>
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#<alt (/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1 (* (/ (+ (* 1/256 (/ (pow Om 8) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 4))) (* 1/8 (/ (* (pow Om 2) (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* Om (pow l 6))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) l)>
#<alt (* -1/2 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))>
#<alt (* -1 (/ (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) l))>
#<alt (* -1 (/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) l))>
#<alt (* -1 (/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1 (* (/ (+ (* 1/256 (/ (pow Om 8) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 4))) (* 1/8 (/ (* (pow Om 2) (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* Om (pow l 6))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) l))>
#<alt (* 1/2 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))>
#<alt (* Om (+ (* -1/16 (* (/ (pow Om 2) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))>
#<alt (* Om (+ (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/16 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 3/256 (* (/ (pow Om 2) (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))>
#<alt (* Om (+ (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/16 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* (pow Om 2) (+ (* -5/2048 (* (/ (pow Om 2) (pow l 7)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 7))))) (* 3/256 (* (/ 1 (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))>
#<alt (+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/2 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))>
#<alt 1>
#<alt (+ 1 (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))>
#<alt (+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))>
#<alt (+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/2 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))>
#<alt (+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (* -2 (* (/ (* (pow kx 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))>
#<alt (+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (* (pow kx 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* -1/2 (* (* (pow kx 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))>
#<alt (+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (* (pow kx 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (* -1/2 (* (* (pow kx 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))>
#<alt (+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (* -2 (* (/ (* (pow ky 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))>
#<alt (+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (* (pow ky 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* -1/2 (* (* (pow ky 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))>
#<alt (+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (* (pow ky 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (* -1/2 (* (* (pow ky 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<alt (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))>
#<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)>

Calls

69 calls:

Time	Variable		Point	Expression
16.0ms	Om	@	0	(pow (/ (* 2 l) Om) 2)
6.0ms	ky	@	inf	(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
5.0ms	kx	@	0	(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
4.0ms	ky	@	-inf	(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
3.0ms	kx	@	inf	(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))

rewrite448.0ms (8.3%)

Memory

-2.0MiB live, 620.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 134×	`accelerator-lowering-fma.f32`
9 134×	`accelerator-lowering-fma.f64`
6 008×	`-lowering-.f32`
6 008×	`-lowering-.f64`
2 908×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	116
1	114	113
2	909	113
0	8496	109

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 639

Calls

Call 1

Inputs
(pow (/ (* 2 l) Om) 2)
(/ 1 2)
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
(pow (sin ky) 2)

Outputs
(exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om))) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om)) (log.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om))))
(neg.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om (-.f64 #s(literal 0 binary64) Om))))
(/.f64 (.f64 #s(literal 2 binary64) l) (/.f64 (.f64 Om Om) (*.f64 #s(literal 2 binary64) l)))
(/.f64 (.f64 #s(literal 2 binary64) l) (.f64 (/.f64 Om (*.f64 #s(literal 2 binary64) l)) Om))
(/.f64 (.f64 #s(literal 2 binary64) l) (neg.f64 (.f64 (/.f64 Om (*.f64 #s(literal 2 binary64) l)) (-.f64 #s(literal 0 binary64) Om))))
(/.f64 (.f64 #s(literal 2 binary64) l) (neg.f64 (/.f64 (.f64 Om Om) (*.f64 l #s(literal -2 binary64)))))
(/.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) (/.f64 Om (.f64 #s(literal 2 binary64) l)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 Om (.f64 #s(literal 2 binary64) l)) Om) (*.f64 #s(literal 2 binary64) l)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 (/.f64 Om (.f64 #s(literal 2 binary64) l)) Om) (*.f64 #s(literal 2 binary64) l)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 Om Om) (.f64 #s(literal 4 binary64) (*.f64 l l))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 Om Om) (.f64 #s(literal 2 binary64) l)) (*.f64 #s(literal 2 binary64) l)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 Om (-.f64 #s(literal 0 binary64) Om)) (neg.f64 (.f64 #s(literal 4 binary64) (*.f64 l l)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 Om Om) (.f64 l #s(literal -2 binary64))) (*.f64 l #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 Om (.f64 l (.f64 (/.f64 l Om) #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) Om) (.f64 (-.f64 #s(literal 0 binary64) l) (.f64 (/.f64 l Om) #s(literal 4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (/.f64 Om (.f64 #s(literal 2 binary64) l)) Om) (*.f64 #s(literal 2 binary64) l))))
(/.f64 (.f64 l #s(literal -2 binary64)) (.f64 (/.f64 Om (*.f64 #s(literal 2 binary64) l)) (-.f64 #s(literal 0 binary64) Om)))
(/.f64 (.f64 l #s(literal -2 binary64)) (/.f64 (.f64 Om Om) (*.f64 l #s(literal -2 binary64))))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(/.f64 (neg.f64 (.f64 #s(literal 4 binary64) (.f64 l l))) (*.f64 Om (-.f64 #s(literal 0 binary64) Om)))
(/.f64 (/.f64 (.f64 l #s(literal -2 binary64)) Om) (/.f64 Om (.f64 l #s(literal -2 binary64))))
(/.f64 (*.f64 (/.f64 l Om) #s(literal 4 binary64)) (/.f64 Om l))
(/.f64 (.f64 l (.f64 (/.f64 l Om) #s(literal 4 binary64))) Om)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) l) (.f64 (/.f64 l Om) #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) Om))
(/.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal -1 binary64)) (/.f64 Om (*.f64 l #s(literal -2 binary64))))
(/.f64 (.f64 (.f64 l (*.f64 (/.f64 l Om) #s(literal 4 binary64))) #s(literal 1 binary64)) Om)
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 #s(literal 4 binary64) (.f64 l l)))) (.f64 Om (-.f64 #s(literal 0 binary64) Om)))
(/.f64 (.f64 (.f64 (/.f64 l Om) #s(literal 4 binary64)) #s(literal 1 binary64)) (/.f64 Om l))
(/.f64 (.f64 (.f64 l (*.f64 (/.f64 l Om) #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) Om))
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))
(pow.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64))
(pow.f64 (/.f64 Om (*.f64 #s(literal 2 binary64) l)) #s(literal -2 binary64))
(pow.f64 (/.f64 (.f64 (/.f64 Om (.f64 #s(literal 2 binary64) l)) Om) (*.f64 #s(literal 2 binary64) l)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om)))
(.f64 #s(literal 2 binary64) (.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) (/.f64 l Om)))
(.f64 #s(literal 2 binary64) (pow.f64 (.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) (/.f64 l Om)) #s(literal 1 binary64)))
(.f64 l (.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) Om)))
(.f64 l (.f64 (/.f64 #s(literal 2 binary64) Om) (/.f64 (*.f64 #s(literal 2 binary64) l) Om)))
(.f64 (.f64 #s(literal 2 binary64) l) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) Om))
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(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))) #s(literal 3 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) #s(literal -1 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 ky))) #s(literal 1 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))))
(-.f64 (/.f64 (cos.f64 #s(literal 0 binary64)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 ky ky)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 ky ky)))))
(/.f64 (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 #s(literal 0 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) (fma.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) (.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 ky ky))) (.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)))))
(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 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 ky)))
(*.f64 (sin.f64 ky) (sin.f64 ky))
(*.f64 (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (sin.f64 ky)))
(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (sin.f64 ky))) (sqrt.f64 (sin.f64 ky)))

simplify502.0ms (9.3%)

Memory

31.8MiB live, 685.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 696×	`accelerator-lowering-fma.f32`
11 696×	`accelerator-lowering-fma.f64`
8 910×	`-lowering-.f32`
8 910×	`-lowering-.f64`
3 486×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	582	10419
1	1932	10186
2	7931	10184
0	8041	9659

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
(* 4 (/ (pow l 2) (pow Om 2)))
1
(+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (* (pow l 2) (+ (* -1 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* -1/4 (* (pow l 2) (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))))))))
(+ 1 (* (pow l 2) (+ (* -1 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow l 2) (+ (* -1/4 (* (pow l 2) (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* 64 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3) (pow Om 6)))))) (* -1/4 (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))))))))))
1/2
(+ 1/2 (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(+ 1/2 (+ (* -1/32 (* (/ (pow Om 3) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(+ 1/2 (+ (* -1/2 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 5))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/32 (* (/ (pow Om 3) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
1/2
(+ 1/2 (* -1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(+ 1/2 (* -1 (/ (+ (* -1/32 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) l)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/32 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) l)))
1/2
(+ 1/2 (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(+ 1/2 (* Om (+ (* -1/32 (* (/ (pow Om 2) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(+ 1/2 (* Om (+ (* 1/4 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/32 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 3/512 (* (/ (pow Om 2) (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5))))))))))
1
(+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))
(+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/4 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))
1
(+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))
(+ 1 (+ (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/4 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/4 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))
(+ (* -1 (* (/ (* (pow kx 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))))
(+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))) (* (pow kx 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* -1/4 (* (* (pow kx 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))
(+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))) (* (pow kx 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* (pow kx 2) (+ (* -1/4 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (* -1/4 (* (* (pow kx 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))
(+ (* -1 (* (/ (* (pow ky 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))))
(+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))) (* (pow ky 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* -1/4 (* (* (pow ky 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))
(+ (* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))) (* (pow ky 2) (+ (* -1 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* (pow ky 2) (+ (* -1/4 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (* -1/4 (* (* (pow ky 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
(* 1/2 (+ 1 (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))))
1
(+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))
(* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))
(* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))
(* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))
(* (pow l 2) (+ (* 4 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (/ 1 (pow l 2))))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(/ (+ (* 4 (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (pow Om 2)) (pow Om 2))
(/ (+ (* 4 (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (pow Om 2)) (pow Om 2))
(/ (+ (* 4 (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (pow Om 2)) (pow Om 2))
1
(+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
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1
(+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
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(+ 1 (+ (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow kx 2) (+ (* -4/3 (/ (* (pow kx 2) (pow l 2)) (pow Om 2))) (* 4 (/ (pow l 2) (pow Om 2)))))))
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1
(+ 1 (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
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(+ 1 (* (pow l 2) (+ (* 2 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow l 2) (+ (* -2 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (* (pow l 2) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)) (pow Om 6))))))))
(* 2 (* (/ l Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* l (+ (* 1/4 (* (/ Om (pow l 2)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* (/ 1 Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* l (+ (* -1/64 (* (/ (pow Om 3) (pow l 4)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (* 1/4 (* (/ Om (pow l 2)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* (/ 1 Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* l (+ (* -1/64 (* (/ (pow Om 3) (pow l 4)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (* 1/512 (* (/ (pow Om 5) (pow l 6)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5))))) (+ (* 1/4 (* (/ Om (pow l 2)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* (/ 1 Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(* -2 (* (/ l Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (* l (+ (* 1/4 (* (/ Om (pow l 2)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* (/ 1 Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* -1 (* l (+ (* -1/64 (* (/ (pow Om 3) (pow l 4)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (* 1/4 (* (/ Om (pow l 2)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* (/ 1 Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
(* -1 (* l (+ (* -1/64 (* (/ (pow Om 3) (pow l 4)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (* 1/512 (* (/ (pow Om 5) (pow l 6)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5))))) (+ (* 1/4 (* (/ Om (pow l 2)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* (/ 1 Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* 2 (* (/ l Om) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (+ (* 1/4 (* (/ (pow Om 2) l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 2 (* l (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) Om)
(/ (+ (* 2 (* l (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow Om 2) (+ (* -1/64 (* (/ (pow Om 2) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) Om)
(/ (+ (* 2 (* l (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow Om 2) (+ (* 1/4 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/64 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/512 (* (/ (pow Om 2) (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))) Om)
1
(+ 1 (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (+ (* -2 (/ (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)) (pow Om 4))) (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(+ 1 (+ (* -2 (/ (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)) (pow Om 4))) (+ (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* 4 (/ (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)) (pow Om 6))))))
1
(+ 1 (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (+ (* -2 (/ (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)) (pow Om 4))) (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(+ 1 (+ (* -2 (/ (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)) (pow Om 4))) (+ (* 2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* 4 (/ (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)) (pow Om 6))))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))
(+ (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (* 2 (* (/ (* (pow kx 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))))
(+ (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (* (pow kx 2) (+ (* 1/2 (* (* (pow kx 2) (- (* -4/3 (/ (pow l 2) (pow Om 2))) (* 4 (/ (pow l 4) (* (pow Om 4) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))) (* 2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))))))
(+ (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (* (pow kx 2) (+ (* 2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))) (* (pow kx 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (- (* -4/3 (/ (pow l 2) (pow Om 2))) (* 4 (/ (pow l 4) (* (pow Om 4) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))))) (* 1/2 (* (* (pow kx 2) (- (* 8/45 (/ (pow l 2) (pow Om 2))) (* 2 (/ (* (pow l 2) (- (* -4/3 (/ (pow l 2) (pow Om 2))) (* 4 (/ (pow l 4) (* (pow Om 4) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))))))))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))
(+ (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (* 2 (* (/ (* (pow ky 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))))
(+ (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (* (pow ky 2) (+ (* 1/2 (* (* (pow ky 2) (- (* -4/3 (/ (pow l 2) (pow Om 2))) (* 4 (/ (pow l 4) (* (pow Om 4) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))) (* 2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))))))
(+ (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (* (pow ky 2) (+ (* 2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))) (* (pow ky 2) (+ (* 1/2 (* (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (- (* -4/3 (/ (pow l 2) (pow Om 2))) (* 4 (/ (pow l 4) (* (pow Om 4) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))))) (* 1/2 (* (* (pow ky 2) (- (* 8/45 (/ (pow l 2) (pow Om 2))) (* 2 (/ (* (pow l 2) (- (* -4/3 (/ (pow l 2) (pow Om 2))) (* 4 (/ (pow l 4) (* (pow Om 4) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))) (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))))))))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(sqrt (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))
(+ (* 4 (/ (* (pow kx 2) (pow l 2)) (pow Om 2))) (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))
(+ (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow kx 2) (+ (* -4/3 (/ (* (pow kx 2) (pow l 2)) (pow Om 2))) (* 4 (/ (pow l 2) (pow Om 2))))))
(+ (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow kx 2) (+ (* 4 (/ (pow l 2) (pow Om 2))) (* (pow kx 2) (+ (* -4/3 (/ (pow l 2) (pow Om 2))) (* 8/45 (/ (* (pow kx 2) (pow l 2)) (pow Om 2))))))))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))
(+ (* 4 (/ (* (pow ky 2) (pow l 2)) (pow Om 2))) (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))
(+ (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))) (* (pow ky 2) (+ (* -4/3 (/ (* (pow ky 2) (pow l 2)) (pow Om 2))) (* 4 (/ (pow l 2) (pow Om 2))))))
(+ (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))) (* (pow ky 2) (+ (* 4 (/ (pow l 2) (pow Om 2))) (* (pow ky 2) (+ (* -4/3 (/ (pow l 2) (pow Om 2))) (* 8/45 (/ (* (pow ky 2) (pow l 2)) (pow Om 2))))))))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
(* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2)))
1
(+ 1 (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (* (pow l 2) (+ (* -2 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* -1/2 (* (pow l 2) (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))))))))
(+ 1 (* (pow l 2) (+ (* -2 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow l 2) (+ (* -1/2 (* (pow l 2) (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* 64 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3) (pow Om 6)))))) (* -1/2 (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))))))))))
(* 1/2 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
(/ (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) l)
(/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) l)
(/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1 (* (/ (+ (* 1/256 (/ (pow Om 8) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 4))) (* 1/8 (/ (* (pow Om 2) (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* Om (pow l 6))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) l)
(* -1/2 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
(* -1 (/ (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))) l))
(* -1 (/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) l))
(* -1 (/ (+ (* -1 (* (/ (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (* Om (pow l 4))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1 (* (/ (+ (* 1/256 (/ (pow Om 8) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 4))) (* 1/8 (/ (* (pow Om 2) (+ (* -1/64 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))) (* 1/256 (/ (pow Om 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* Om (pow l 6))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (+ (* -1/16 (* (/ (pow Om 3) (pow l 2)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* Om (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))) l))
(* 1/2 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))
(* Om (+ (* -1/16 (* (/ (pow Om 2) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* Om (+ (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/16 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 3/256 (* (/ (pow Om 2) (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))
(* Om (+ (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/16 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* (pow Om 2) (+ (* -5/2048 (* (/ (pow Om 2) (pow l 7)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 7))))) (* 3/256 (* (/ 1 (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))))
1
(+ 1 (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))
(+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/2 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))
1
(+ 1 (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4)))))
(+ 1 (+ (* -2 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (+ (* -1/2 (/ (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (pow Om 4))) (* -1/2 (/ (+ (* 2 (* (pow l 2) (* (+ (* -16 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2))) (* 4 (* (pow l 4) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 64 (* (pow l 6) (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3)))) (pow Om 6))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))
(+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (* -2 (* (/ (* (pow kx 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))
(+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (* (pow kx 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* -1/2 (* (* (pow kx 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))
(+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))))) (* (pow kx 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (* -1/2 (* (* (pow kx 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))))))))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))
(+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (* -2 (* (/ (* (pow ky 2) (pow l 2)) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))
(+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (* (pow ky 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* -1/2 (* (* (pow ky 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))
(+ (sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))))) (* (pow ky 2) (+ (* -2 (* (/ (pow l 2) (pow Om 2)) (sqrt (/ 1 (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (* -1/2 (* (* (pow ky 2) (+ (* -4 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (+ (* 8/45 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (+ (* 2 (/ (* (pow l 2) (+ (* -16 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))) (+ (* -4/3 (/ (pow l 2) (* (pow Om 2) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 2)))) (* 4 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3))))))) (* (pow Om 2) (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))) (* 16/3 (/ (pow l 4) (* (pow Om 4) (pow (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2)))) 3)))))))) (sqrt (+ 1 (* 4 (/ (* (pow l 2) (pow (sin kx) 2)) (pow Om 2))))))))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)

Outputs
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
(* 4 (/ (pow l 2) (pow Om 2)))
(/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)))
(+ 1 (* (pow l 2) (+ (* -1 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* -1/4 (* (pow l 2) (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))))))))
(fma.f64 (.f64 l l) (fma.f64 (.f64 l l) (.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 Om #s(literal 4 binary64))) #s(literal 3 binary64)) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (neg.f64 (.f64 Om Om)))) #s(literal 1 binary64))
(+ 1 (* (pow l 2) (+ (* -1 (/ (+ (pow (sin kx) 2) (pow (sin ky) 2)) (pow Om 2))) (* (pow l 2) (+ (* -1/4 (* (pow l 2) (+ (* 2 (/ (* (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4)))) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))) (* 64 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3) (pow Om 6)))))) (* -1/4 (+ (* -16 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))) (* 4 (/ (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 2) (pow Om 4))))))))))
(fma.f64 (.f64 l l) (-.f64 (.f64 (.f64 l l) (fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 l l) (fma.f64 #s(literal 2 binary64) (.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 Om #s(literal 4 binary64))) (.f64 #s(literal -12 binary64) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 Om Om)))) (/.f64 (.f64 #s(literal 64 binary64) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 3 binary64))) (pow.f64 Om #s(literal 6 binary64))))) (.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 Om #s(literal 4 binary64))) #s(literal 3 binary64)))) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 Om Om))) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (/.f64 Om l) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (+ (* -1/32 (* (/ (pow Om 3) (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 1/4 (* (/ Om l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(fma.f64 Om (.f64 (/.f64 #s(literal 1/4 binary64) l) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 3 binary64)))) (.f64 (/.f64 (.f64 Om (.f64 Om Om)) (.f64 l (.f64 l l))) #s(literal -1/32 binary64)) #s(literal 1/2 binary64)))
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1/2
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#s(literal 1/2 binary64)
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1
#s(literal 1 binary64)
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1
#s(literal 1 binary64)
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#s(literal 1 binary64)
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(* Om (+ (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/16 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* 3/256 (* (/ (pow Om 2) (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))
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(* Om (+ (* 1/2 (* (/ 1 l) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow Om 2) (+ (* -1/16 (* (/ 1 (pow l 3)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 3))))) (* (pow Om 2) (+ (* -5/2048 (* (/ (pow Om 2) (pow l 7)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 7))))) (* 3/256 (* (/ 1 (pow l 5)) (sqrt (/ 1 (pow (+ (pow (sin kx) 2) (pow (sin ky) 2)) 5)))))))))))
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(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (/ 1 (+ 1 (* 4 (/ (* (pow l 2) (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow Om 2))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4 binary64) (/.f64 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 Om Om)) #s(literal 1 binary64))))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(.f64 ky (.f64 ky (fma.f64 (*.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(.f64 ky (.f64 ky (fma.f64 (.f64 ky ky) (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) #s(literal 1 binary64))))
(* (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))

eval152.0ms (2.8%)

Memory: -3.0MiB live, 261.5MiB allocated
Compiler: Compiled 46 172 to 5 337 computations (88.4% saved)

prune129.0ms (2.4%)

Memory

33.8MiB live, 231.0MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	906	9	915
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	907	9	916

Accuracy

100.0%

Counts

916 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	82.8%	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (/.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (*.f64 Om Om)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
▶	68.6%	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (/.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 Om Om)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
	76.3%	(sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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))))) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
	49.9%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))))
▶	60.3%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64))))))))
▶	91.6%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 (/.f64 l Om) #s(literal 4 binary64)) (.f64 (/.f64 l Om) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))) #s(literal 1 binary64)))))))
▶	82.5%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 Om Om))))))))
	61.7%	(sqrt.f64 #s(literal 1 binary64))
▶	56.1%	(sqrt.f64 #s(literal 1/2 binary64))

Compiler

Compiled 498 to 342 computations (31.3% saved)

simplify777.0ms (14.4%)

Memory

-36.1MiB live, 935.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	320	(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64)))))))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
✓	cost-diff	2240	(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))) (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (.f64 Om Om)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64)))
✓	cost-diff	0	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 Om Om))))))))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 Om Om)))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 Om Om)))))))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (/.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 Om Om)) #s(literal 1 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (/.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 Om Om)) #s(literal 1 binary64))))
✓	cost-diff	0	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (/.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 Om Om)) #s(literal 1 binary64)))) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (/.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 Om Om)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 (/.f64 l Om) #s(literal 4 binary64)) (.f64 (/.f64 l Om) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))) #s(literal 1 binary64))))))
✓	cost-diff	384	(+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))
✓	cost-diff	704	(fma.f64 (.f64 (/.f64 l Om) #s(literal 4 binary64)) (.f64 (/.f64 l Om) (+.f64 (+.f64 #s(literal 1/2 binary64) (.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)))))) #s(literal 1 binary64))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))

Rules

27 362×	`accelerator-lowering-fma.f32`
27 362×	`accelerator-lowering-fma.f64`
6 714×	`+-lowering-+.f64`
6 714×	`+-lowering-+.f32`
6 108×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	889
1	166	849
2	610	819
3	2484	819
4	5714	819
5	6065	819
6	6111	819
7	6116	819
8	6118	819
9	6118	795
0	9406	750

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1)))))
(/ 1 2)
1
2
(+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1))))
(/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1)))
(sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1))
(+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1)
(* (/ l Om) 4)
(/ l Om)
l
Om
4
(* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))
(+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky)))))
(+ 1/2 (* -1/2 (cos (+ kx kx))))
1/2
(* -1/2 (cos (+ kx kx)))
-1/2
(cos (+ kx kx))
(+ kx kx)
kx
(+ 1/2 (* -1/2 (cos (+ ky ky))))
(* -1/2 (cos (+ ky ky)))
(cos (+ ky ky))
(+ ky ky)
ky
(sqrt 1/2)
1/2
(sqrt (+ (* 1/2 (sqrt (/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1)))) 1/2))
(+ (* 1/2 (sqrt (/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1)))) 1/2)
1/2
(sqrt (/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1)))
(/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1))
1
(+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1)
(* 4 (* l l))
4
(* l l)
l
(/ (pow (sin kx) 2) (* Om Om))
(pow (sin kx) 2)
(sin kx)
kx
2
(* Om Om)
Om
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om)))))))
(/ 1 2)
1
2
(+ 1 (/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))))))
(/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om)))))
(sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))))
(+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om)))
(/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))
(* (* 4 (* l l)) (pow (sin ky) 2))
(* 4 (* l l))
4
(* l l)
l
(pow (sin ky) 2)
(sin ky)
ky
(* Om Om)
Om
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1))))))
(/ 1 2)
1
2
(+ 1 (/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)))))
(/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1))))
(sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)))
(+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1))
(/ (* 4 (* l l)) (* Om Om))
(* 4 (* l l))
4
(* l l)
l
(* Om Om)
Om
(+ 1/2 (* -1/2 (cos (+ ky ky))))
1/2
(* -1/2 (cos (+ ky ky)))
-1/2
(cos (+ ky ky))
(+ ky ky)
ky
(+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)
(+ 1/2 (* -1/2 (cos (+ kx kx))))
(* -1/2 (cos (+ kx kx)))
(cos (+ kx kx))
(+ kx kx)
kx

Outputs
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64)))))
(/ 1 2)
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)
(+ 1 (/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64)))))
(/ 1 (sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1))
(sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64)))
(+ (* (* (/ l Om) 4) (* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))) 1)
(fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64))
(* (/ l Om) 4)
(*.f64 l (/.f64 #s(literal 4 binary64) Om))
(/ l Om)
(/.f64 l Om)
l
Om
4
#s(literal 4 binary64)
(* (/ l Om) (+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky))))))
(*.f64 (/.f64 l Om) (fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)))
(+ (+ 1/2 (* -1/2 (cos (+ kx kx)))) (+ 1/2 (* -1/2 (cos (+ ky ky)))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 1 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
#s(literal 1/2 binary64)
(* -1/2 (cos (+ kx kx)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))
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#s(literal -1/2 binary64)
(cos (+ kx kx))
(cos.f64 (+.f64 kx kx))
(+ kx kx)
(+.f64 kx kx)
kx
(+ 1/2 (* -1/2 (cos (+ ky ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))
(* -1/2 (cos (+ ky ky)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
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(sqrt 1/2)
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(+ (* 1/2 (sqrt (/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1)))) 1/2)
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64)))) #s(literal 1/2 binary64))
1/2
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(/ 1 (+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1))
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#s(literal 1 binary64)
(+ (* (* 4 (* l l)) (/ (pow (sin kx) 2) (* Om Om))) 1)
(fma.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64))
(* 4 (* l l))
(.f64 #s(literal 4 binary64) (.f64 l l))
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#s(literal 4 binary64)
(* l l)
(*.f64 l l)
l
(/ (pow (sin kx) 2) (* Om Om))
(/.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 Om Om))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin kx)
(sin.f64 kx)
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(* Om Om)
(*.f64 Om Om)
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(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om)))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64)))))
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(/ 1 (sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))))
(sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64)))
(+ 1 (/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om)))
(fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 l l)) (*.f64 Om Om)) #s(literal 1 binary64))
(/ (* (* 4 (* l l)) (pow (sin ky) 2)) (* Om Om))
(/.f64 (.f64 l (.f64 (.f64 #s(literal 4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) l)) (.f64 Om Om))
(* (* 4 (* l l)) (pow (sin ky) 2))
(.f64 l (.f64 (*.f64 #s(literal 4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) l))
(* 4 (* l l))
(.f64 #s(literal 4 binary64) (.f64 l l))
4
#s(literal 4 binary64)
(* l l)
(*.f64 l l)
l
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin ky)
(sin.f64 ky)
ky
(* Om Om)
(*.f64 Om Om)
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(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64))))))
(* (/ 1 2) (+ 1 (/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64)))))
(/ 1 2)
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)
(+ 1 (/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64)))))
(/ 1 (sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64))))
(sqrt (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ ky ky))))) (+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)))
(sqrt.f64 (fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64)))
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(fma.f64 (.f64 l l) (/.f64 (fma.f64 #s(literal -2 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 ky ky))) #s(literal 4 binary64)) (.f64 Om Om)) #s(literal 1 binary64))
(/ (* 4 (* l l)) (* Om Om))
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(* 4 (* l l))
(.f64 #s(literal 4 binary64) (.f64 l l))
4
#s(literal 4 binary64)
(* l l)
(*.f64 l l)
l
(* Om Om)
(*.f64 Om Om)
Om
(+ 1/2 (* -1/2 (cos (+ ky ky))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))
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(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky)))
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(+.f64 ky ky)
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(+ (* (/ (* 4 (* l l)) (* Om Om)) (+ 1/2 (* -1/2 (cos (+ kx kx))))) 1)
(fma.f64 (/.f64 (.f64 l l) (.f64 Om Om)) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal -2 binary64) #s(literal 2 binary64)) #s(literal 1 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)))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx)))
(cos (+ kx kx))
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kx

localize2.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated

Samples

1.0ms

1×

valid

Compiler

Compiled 943 to 65 computations (93.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

ival-pow2: 0.0ms (0% of total)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze146.0ms (2.7%)

sample2.2s (40.6%)

preprocess298.0ms (5.5%)

explain366.0ms (6.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify225.0ms (4.2%)

localize77.0ms (1.4%)

series76.0ms (1.4%)

rewrite448.0ms (8.3%)

simplify502.0ms (9.3%)

eval152.0ms (2.8%)

prune129.0ms (2.4%)

simplify777.0ms (14.4%)

localize2.0ms (0%)

end0.0ms (0%)

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