Metrics for Beckmann Sample, normalization factor

analyze30.0ms (0.2%)

Memory

-20.9MiB live, 55.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.3%	87.7%	0%	0%	0%	0
0%	0%	12.3%	87.7%	0%	0%	0%	1
50%	6.2%	6.2%	87.7%	0%	0%	0%	2
50%	6.2%	6.2%	87.7%	0%	0%	0%	3
75%	9.2%	3.1%	87.7%	0%	0%	0%	4
75%	9.2%	3.1%	87.7%	0%	0%	0%	5
87.5%	10.8%	1.5%	87.7%	0%	0%	0%	6
87.5%	10.8%	1.5%	87.7%	0%	0%	0%	7
93.8%	11.5%	0.8%	87.7%	0%	0%	0%	8
93.8%	11.5%	0.8%	87.7%	0%	0%	0%	9
96.9%	11.9%	0.4%	87.7%	0%	0%	0%	10
96.9%	11.9%	0.4%	87.7%	0%	0%	0%	11
98.4%	12.1%	0.2%	87.7%	0%	0%	0%	12

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.1s (14.8%)

Memory

78.4MiB live, 2 817.3MiB allocated

Samples

1.4s	8 256×	0	valid
10.0ms	75×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 243.0ms (20.2% of total)

ival-div: 184.0ms (15.3% of total)

ival-mult: 148.0ms (12.3% of total)

ival-add: 133.0ms (11% of total)

const: 133.0ms (11% of total)

ival-<: 97.0ms (8.1% of total)

ival-sub: 87.0ms (7.2% of total)

ival-exp: 73.0ms (6.1% of total)

ival-neg: 35.0ms (2.9% of total)

ival-pi: 32.0ms (2.7% of total)

ival-and: 22.0ms (1.8% of total)

exact: 14.0ms (1.2% of total)

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

Bogosity

preprocess271.0ms (1.9%)

Memory

3.5MiB live, 158.7MiB allocated

Algorithm

1×	egg-herbie

Rules

1 608×	`lower-fma.f64`
1 608×	`lower-fma.f32`
1 466×	`div-sub`
1 040×	`lower-*.f64`
1 034×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	127
1	135	117
2	394	111
3	1316	110
4	3697	110
5	5276	110
6	7001	110
7	7750	110
0	18	25
0	33	25
1	59	23
2	122	22
3	242	22
4	365	22
5	743	22
6	1884	22
7	2802	22
8	3446	22
9	4078	22
10	4247	22
11	4282	22
12	4315	22
13	4449	22
14	5068	22
15	5076	22
16	5080	22
17	5080	22
0	5080	21

Stop Event

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

Calls

Call 1

Inputs

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)))

explain269.0ms (1.9%)

Memory

-36.6MiB live, 427.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
1	-	-	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
0	-	-	`(sqrt.f32 (PI.f32))`
0	-	-	`(PI.f32)`
0	-	-	`(*.f32 (neg.f32 cosTheta) cosTheta)`
0	-	-	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`
0	-	-	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
0	-	-	`(+.f32 #s(literal 1 binary32) c)`
0	-	-	`cosTheta`
0	-	-	`(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))`
0	-	-	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
0	-	-	`c`
0	-	-	`(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))`
0	-	-	`(-.f32 #s(literal 1 binary32) cosTheta)`
0	-	-	`(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)`
0	-	-	`#s(literal 1 binary32)`
0	-	-	`(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)`
0	-	-	`(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))`
0	-	-	`(neg.f32 cosTheta)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f32`	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`	n/o	1	0
↳	`(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)`	overflow	1
↳	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`	overflow	1
↳	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`	overflow	1
↳	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`	overflow	1

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

91.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

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

ival-neg: 20.0ms (27.8% of total)

ival-sub: 13.0ms (18.1% of total)

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

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

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

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

ival-exp: 4.0ms (5.6% of total)

ival-pi: 2.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

97.5%

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify167.0ms (1.2%)

Memory

29.9MiB live, 146.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	64	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	352	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))

Rules

1 608×	`lower-fma.f64`
1 608×	`lower-fma.f32`
1 040×	`lower-*.f64`
1 034×	`lower-*.f32`
978×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	126
0	33	126
1	59	118
2	122	115
3	242	115
4	365	115
5	743	115
6	1884	115
7	2802	115
8	3446	115
9	4078	115
10	4247	115
11	4282	115
12	4315	115
13	4449	115
14	5068	115
15	5076	115
16	5080	115
17	5080	115
0	5080	108

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)

Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c))
(+.f32 #s(literal 1 binary32) c)
c
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 cosTheta (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta)))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 (neg.f32 cosTheta) cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(neg.f32 cosTheta)

localize65.0ms (0.5%)

Memory

-24.9MiB live, 128.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.2%	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))

Samples

36.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

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

ival-sub: 7.0ms (27% of total)

ival-div: 5.0ms (19.3% of total)

ival-mult: 4.0ms (15.4% of total)

ival-sqrt: 4.0ms (15.4% of total)

ival-add: 3.0ms (11.6% of total)

ival-exp: 2.0ms (7.7% of total)

ival-pi: 1.0ms (3.9% of total)

ival-neg: 1.0ms (3.9% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

12.2MiB live, 49.7MiB allocated

Counts

6 → 84

Calls

Call 1

Inputs
#<alt (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))>
#<alt (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))>
#<alt (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))>
#<alt (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))>
#<alt (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)>

Outputs
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)>
#<alt (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))>
#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)>
#<alt (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))>
#<alt (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))>
#<alt (+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))>
#<alt (+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))>
#<alt (/ 1 c)>
#<alt (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)>
#<alt (/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)>
#<alt (/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)>
#<alt (/ 1 c)>
#<alt (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))>
#<alt (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))>
#<alt (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))>
#<alt (- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))>
#<alt (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))>
#<alt (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt c>
#<alt (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)>
#<alt (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))>
#<alt (+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))>
#<alt (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))>
#<alt (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))>
#<alt (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))>
#<alt (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))>
#<alt 1>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (* -2 cosTheta)>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* -2 cosTheta)>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>

Calls

21 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
4.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
2.0ms	cosTheta	@	inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
2.0ms	cosTheta	@	-inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
1.0ms	cosTheta	@	-inf	(* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))

rewrite300.0ms (2.1%)

Memory

4.3MiB live, 714.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 132×	`lower-fma.f64`
4 132×	`lower-fma.f32`
3 752×	`lower-*.f64`
3 746×	`lower-*.f32`
3 536×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	89
0	33	89
1	141	80
2	1060	73
0	8552	73

Stop Event

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

Counts

6 → 473

Calls

Call 1

Inputs
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)

Outputs
(neg.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (neg.f32 cosTheta)))
(pow.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) #s(literal -1 binary32))
(-.f32 (/.f32 #s(literal 0 binary32) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (neg.f32 cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 cosTheta (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))))
(/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (*.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))))))
(/.f32 (neg.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
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(/.f32 (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (pow.f32 (neg.f32 (.f32 cosTheta cosTheta)) #s(literal 3 binary32))) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (-.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 (fma.f32 cosTheta (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))) (fma.f32 cosTheta cosTheta (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (*.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 3 binary32)) (pow.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (*.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))))
(/.f32 (-.f32 (pow.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta) (.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (neg.f32 (.f32 cosTheta cosTheta)))) (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (.f32 cosTheta cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 (neg.f32 cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (+.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(*.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))
(*.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 4 binary32) (.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta)))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (fma.f32 cosTheta cosTheta (*.f32 (neg.f32 (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(*.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) #s(literal -1 binary32))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (fma.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta cosTheta)) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta cosTheta))))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 4 binary32) (*.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))

simplify458.0ms (3.2%)

Memory

27.4MiB live, 835.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 656×	`lower-fma.f64`
9 656×	`lower-fma.f32`
5 090×	`lower-*.f64`
5 090×	`lower-*.f32`
4 540×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 82

Calls

Call 1

Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))
1
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* -2 cosTheta)
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 cosTheta (*.f32 cosTheta #s(literal -1/2 binary32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -1/2 binary32) #s(literal -1/2 binary32)))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (*.f32 (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/8 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(fma.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/8 binary32))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (*.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 #s(literal -1 binary32)) (neg.f32 (.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 #s(literal -1 binary32)) (neg.f32 (.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) #s(literal -1/16 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32)) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(neg.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
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c
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (+.f32 #s(literal 1 binary32) c))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32)) c)))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32)) c))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32)) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))))) (+.f32 #s(literal 1 binary32) c))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 binary32)) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c)))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
(+.f32 (+.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c)) (fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/8 binary32) (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))
(+.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 binary32)) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) #s(literal -1/16 binary32))))))
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))

eval79.0ms (0.6%)

Memory: 1.3MiB live, 155.5MiB allocated
Compiler: Compiled 23 190 to 2 839 computations (87.8% saved)

prune158.0ms (1.1%)

Memory

-10.8MiB live, 189.0MiB allocated

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	533	22	555
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	534	22	556

Accuracy

99.9%

Counts

556 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	92.4%	(pow.f32 (pow.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	49.3%	(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (*.f32 cosTheta cosTheta))))))))
	93.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c)))
	97.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	52.9%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
▶	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
▶	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	4.9%	(/.f32 #s(literal 1 binary32) c)
	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	85.2%	(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))

Compiler

Compiled 1 044 to 644 computations (38.3% saved)

simplify356.0ms (2.5%)

Memory

-36.1MiB live, 442.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
✓	cost-diff	64	(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
✓	cost-diff	192	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))
✓	cost-diff	0	(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
✓	cost-diff	512	(fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	736	(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	cost-diff	0	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
✓	cost-diff	64	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	64	(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	64	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Rules

11 336×	`lower-fma.f64`
11 330×	`lower-fma.f32`
3 160×	`lower-*.f64`
3 146×	`lower-*.f32`
1 788×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	495
0	94	495
1	174	495
2	376	468
3	869	468
4	2701	468
5	5763	468
0	8238	435

Stop Event

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

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))
(cbrt.f32 (PI.f32))
(PI.f32)
#s(literal -3/2 binary32)
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(/.f32 #s(literal 1 binary32) c)
#s(literal 1 binary32)
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
(+.f32 #s(literal 1 binary32) c)
c
(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
#s(literal 1 binary32)
(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
cosTheta
(fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))))
(+.f32 #s(literal 1 binary32) c)
c
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))
(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
(.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))
(sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))
(+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))
(+.f32 cosTheta cosTheta)
cosTheta
(exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))
(neg.f32 (*.f32 cosTheta cosTheta))
(*.f32 cosTheta cosTheta)

Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c))
(+.f32 #s(literal 1 binary32) c)
c
(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))
(cbrt.f32 (PI.f32))
(PI.f32)
#s(literal -3/2 binary32)
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta)
(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 (neg.f32 cosTheta) cosTheta)
(*.f32 cosTheta (neg.f32 cosTheta))
(neg.f32 cosTheta)
(/.f32 #s(literal 1 binary32) c)
#s(literal 1 binary32)
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) c))
(+.f32 #s(literal 1 binary32) c)
c
(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 cosTheta (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 c cosTheta))))
#s(literal 1 binary32)
(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(/.f32 (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 c cosTheta))) cosTheta)
(+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 c cosTheta)))
cosTheta
(fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 c cosTheta))
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) c)
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))))
(fma.f32 (sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(+.f32 #s(literal 1 binary32) c)
c
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))
(/.f32 (sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))
(.f32 (exp.f32 (.f32 cosTheta cosTheta)) (/.f32 (*.f32 cosTheta (sqrt.f32 (PI.f32))) (sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta)))))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
(/.f32 (sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))
(.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))
(.f32 (sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))
(sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))
(sqrt.f32 (+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta)))
(+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))
(+.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))
(+.f32 cosTheta cosTheta)
cosTheta
(exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(neg.f32 (*.f32 cosTheta cosTheta))
(*.f32 cosTheta (neg.f32 cosTheta))
(*.f32 cosTheta cosTheta)

localize226.0ms (1.6%)

Memory

11.9MiB live, 281.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))
✓	accuracy	99.6%	(fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
✓	accuracy	98.3%	(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.6%	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
✓	accuracy	98.3%	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.9%	(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.2%	(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))

Samples

132.0ms

256×

valid

Compiler

Compiled 513 to 53 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-mult: 45.0ms (45.1% of total)

ival-div: 18.0ms (18% of total)

ival-add: 11.0ms (11% of total)

ival-sqrt: 7.0ms (7% of total)

ival-pow: 5.0ms (5% of total)

ival-exp: 4.0ms (4% of total)

ival-sub: 4.0ms (4% of total)

ival-cbrt: 2.0ms (2% of total)

ival-neg: 2.0ms (2% of total)

ival-pi: 1.0ms (1% of total)

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

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

exact: 0.0ms (0% of total)

series64.0ms (0.4%)

Memory

8.6MiB live, 121.1MiB allocated

Counts

20 → 336

Calls

Call 1

Inputs
#<alt (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))>
#<alt (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))>
#<alt (+.f32 #s(literal 1 binary32) c)>
#<alt (/.f32 #s(literal 1 binary32) c)>
#<alt (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))>
#<alt (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)>
#<alt (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))>
#<alt (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))>
#<alt (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))>
#<alt (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)>
#<alt (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))>
#<alt (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))>
#<alt (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))>
#<alt (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))>
#<alt (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)>
#<alt (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))>
#<alt (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))>

Outputs
#<alt (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))>
#<alt (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt c>
#<alt (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)>
#<alt (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))>
#<alt (+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))>
#<alt (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))>
#<alt (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))>
#<alt (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))>
#<alt (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)>
#<alt (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))>
#<alt (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
#<alt (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))>
#<alt (+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))>
#<alt (+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))>
#<alt (/ 1 c)>
#<alt (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)>
#<alt (/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)>
#<alt (/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)>
#<alt (/ 1 c)>
#<alt (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))>
#<alt (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))>
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#<alt (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2)))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))))) (* (sqrt 2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))) (+ (* -1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))))))>
#<alt (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt -2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1)))))))))>
#<alt (- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt -2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3)))))))) (* (sqrt -2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt -2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (* 1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3)))))))))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)>
#<alt (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))>
#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))>
#<alt 1>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (* -2 cosTheta)>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* -2 cosTheta)>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (sqrt (/ 1 (PI)))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (* -1 (* cosTheta (sqrt (/ 1 (PI)))))>
#<alt (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))>
#<alt (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))>
#<alt (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))>
#<alt (* -1 (* cosTheta (sqrt (/ 1 (PI)))))>
#<alt (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>
#<alt (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>
#<alt (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>

Calls

84 calls:

Time	Variable		Point	Expression
8.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))))
6.0ms	cosTheta	@	-inf	(/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))
5.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))))
3.0ms	cosTheta	@	0	(/ 1 (+ (+ 1 c) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta)))
3.0ms	cosTheta	@	0	(+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))

rewrite362.0ms (2.5%)

Memory

6.8MiB live, 401.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 824×	`lower-*.f64`
3 810×	`lower-*.f32`
3 480×	`lower-fma.f64`
3 474×	`lower-fma.f32`
3 064×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	314
0	94	314
1	407	273
2	3532	249
0	8201	247

Stop Event

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

Counts

20 → 568

Calls

Call 1

Inputs
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(+.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) c)
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))
(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))
(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))

Outputs
(exp.f32 (neg.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) c)) #s(literal -1 binary32))))
(+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) c))
(+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))))
(+.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))) (+.f32 #s(literal 1 binary32) c))
(+.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) c) #s(literal 1 binary32))
(+.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) #s(literal 1 binary32)) c)
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (+.f32 #s(literal 1 binary32) c))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))) (-.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))) #s(literal 3 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta))) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (*.f32 cosTheta (neg.f32 cosTheta))))))) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) c (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))))))
(fma.f32 c #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))))))
(fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (fma.f32 c (.f32 c c) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))
(fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))
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(exp.f32 (fma.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32)) (*.f32 (log1p.f32 (+.f32 cosTheta cosTheta)) #s(literal 1/2 binary32))))
(exp.f32 (fma.f32 (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))) #s(literal -3/4 binary32) (.f32 (*.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))) #s(literal -3/4 binary32))))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -3/4 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/4 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/4 binary32))
(pow.f32 (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) #s(literal 1/2 binary32))
(pow.f32 (exp.f32 #s(literal -3/2 binary32)) (*.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (neg.f32 (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -3/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -3/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) #s(literal -3/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/9 binary32)) #s(literal -3/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -2/3 binary32)) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)) #s(literal -1/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 #s(literal 1 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 #s(literal 1 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -3/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -3/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -3/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -3/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) #s(literal -3/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/9 binary32)) #s(literal -3/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/9 binary32)) #s(literal -3/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/9 binary32)) #s(literal -3/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -2/3 binary32)) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -2/3 binary32)) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(fma.f32 (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 (+.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta))))
(/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta (*.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) cosTheta))
(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))

simplify470.0ms (3.3%)

Memory

20.9MiB live, 791.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 062×	`lower-*.f64`
7 062×	`lower-*.f32`
6 942×	`lower-fma.f64`
6 942×	`lower-fma.f32`
5 092×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1271	11675
1	4193	11304
0	8868	10791

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 326

Calls

Call 1

Inputs
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
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(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))) c))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))) c))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))) c))))
(* c cosTheta)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))) c)))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* -4 (/ (* (PI) (- (* -1 (- c (sqrt (/ 1 (PI))))) 1)) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
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(/ 1 c)
(/ (- (+ 1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
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(/ 1 c)
(* -1 (/ (- (* -1 (/ (- (sqrt (/ 1 (PI))) (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (/ (* (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))) (- (sqrt (/ 1 (PI))) (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))) (* c cosTheta)))) (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (/ (- (* -1 (/ (* (pow (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))) 2) (- (sqrt (/ 1 (PI))) (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))) (* c (pow cosTheta 2)))) (* -1 (/ (* (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))) (- (sqrt (/ 1 (PI))) (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))) cosTheta))) c))) (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) c)) 1) c))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))) (sqrt (/ 1 (PI)))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (- (+ (* -1 (/ (- c (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) (/ 1 cosTheta)) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* -1 (- c (sqrt (/ 1 (PI))))) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))) cosTheta)
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c
(* c (- (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(* c (- (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
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c
(* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))
(* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))
(* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* 1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2)))
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(* cosTheta (sqrt (PI)))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* cosTheta (+ (sqrt (PI)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI))))) (* cosTheta (+ (* -1 (sqrt (PI))) (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (+ (* -4 (PI)) (* 8 (PI)))))))))))))))
(* (sqrt (* cosTheta (PI))) (/ (sqrt 1/2) (exp (neg (pow cosTheta 2)))))
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(* (sqrt (* cosTheta (PI))) (/ (* (sqrt -1) (sqrt -1/2)) (exp (neg (pow cosTheta 2)))))
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(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (/ (* (sqrt -1) (sqrt -1/2)) (exp (neg (pow cosTheta 2)))))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (+ (* -1/64 (/ (* cosTheta (PI)) (pow (sqrt -1/2) 2))) (* 1/16 (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -1/2))))) (* 1/16 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (* (exp (neg (pow cosTheta 2))) (sqrt -1/2)))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (* (exp (neg (pow cosTheta 2))) (sqrt -1/2)))))))))
(/ 1 cosTheta)
(/ (+ 1 cosTheta) cosTheta)
(/ (+ 1 (* cosTheta (+ 1 (* -3/2 cosTheta)))) cosTheta)
(/ (+ 1 (* cosTheta (+ 1 (* cosTheta (- (* -1/2 cosTheta) 3/2))))) cosTheta)
(* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt 2)))
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(* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1)))))
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(/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))))
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(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* 1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))))) (* (sqrt 2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))) (+ (* -1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))) 2))))))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt -2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1)))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt -2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3)))))))) (* (sqrt -2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt -2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 2))))) (* 1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))))) 3)))))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
1
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* -2 cosTheta)
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))

Outputs
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c))
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(+.f32 c (fma.f32 c (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (*.f32 cosTheta c)) #s(literal 1 binary32)))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(+.f32 c (fma.f32 c (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (*.f32 cosTheta c)) #s(literal 1 binary32)))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(+.f32 c (fma.f32 c (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (*.f32 cosTheta c)) #s(literal 1 binary32)))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(neg.f32 (fma.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) c (neg.f32 c)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(neg.f32 (fma.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) c (neg.f32 c)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(neg.f32 (fma.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) c (neg.f32 c)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)))) cosTheta)) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (+.f32 c (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) c))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 #s(literal 1/16 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))))))))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) c))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))
(+.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) c) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32))))))
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(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta c)) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2) c) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 3) c) (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2)) c)) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))) c) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
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(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))
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(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
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(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
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(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(- c (sqrt (/ 1 (PI))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))
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(- (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) (sqrt (/ 1 (PI))))
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(- (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) (sqrt (/ 1 (PI))))
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(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
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(* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
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(* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
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(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
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(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (- c (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
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(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (- c (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta))) (neg.f32 cosTheta))))
(- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))
(fma.f32 cosTheta (*.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(- (+ c (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))
(-.f32 (fma.f32 cosTheta (*.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ c (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))
(-.f32 (fma.f32 cosTheta (*.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ c (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))
(-.f32 (fma.f32 cosTheta (*.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(* c (- (+ 1 (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(+.f32 c (.f32 c (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* c (- (+ 1 (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(+.f32 c (.f32 c (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* c (- (+ 1 (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(+.f32 c (.f32 c (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
c
(* -1 (* c (- (* -1 (/ (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))) c)) 1)))
(.f32 (+.f32 (neg.f32 (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))) c)) 1)))
(.f32 (+.f32 (neg.f32 (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))) c)) 1)))
(.f32 (+.f32 (neg.f32 (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)) #s(literal -1 binary32)) (neg.f32 c))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- c (sqrt (/ 1 (PI))))))
(fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))))
(fma.f32 cosTheta (-.f32 (fma.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) (sqrt (/ 1 (PI))))))
(fma.f32 cosTheta (-.f32 (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal -3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32))))
(* (pow cosTheta 3) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal -3/2 binary32) (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 c (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 3) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal -3/2 binary32) (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (+.f32 (/.f32 c (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))))
(* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* -1 (* (pow cosTheta 3) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* 3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(neg.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal 3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)))))
(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (- (+ (* -3/2 (sqrt (/ 1 (PI)))) (/ c cosTheta)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
(.f32 (.f32 cosTheta (*.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) (neg.f32 cosTheta)))))
(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- c (sqrt (/ 1 (PI)))))) cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (/.f32 (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (neg.f32 (.f32 cosTheta (*.f32 cosTheta cosTheta))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))
(fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta c)))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta c)))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta c)))
(* c cosTheta)
(*.f32 cosTheta c)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))) c))))
(.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))) c))))
(.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))) c))))
(.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))) c)))))
(neg.f32 (.f32 c (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))) c)))))
(neg.f32 (.f32 c (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))) c)))))
(neg.f32 (.f32 c (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (-.f32 (.f32 cosTheta (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32))))) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)))) (neg.f32 (sqrt.f32 (PI.f32))) (fma.f32 #s(literal 3/2 binary32) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32))))) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32))))) (neg.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (fma.f32 #s(literal 2 binary32) (sqrt.f32 (PI.f32)) (.f32 #s(literal 6 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))) (.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 (fma.f32 #s(literal 4 binary32) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32))) (.f32 cosTheta (neg.f32 cosTheta))) (fma.f32 #s(literal 2 binary32) (sqrt.f32 (PI.f32)) (.f32 #s(literal 6 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta)))) (.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) (pow cosTheta 2)))))) (pow cosTheta 2))
(/.f32 (-.f32 (fma.f32 #s(literal 2 binary32) (sqrt.f32 (PI.f32)) (/.f32 (fma.f32 #s(literal 3 binary32) (fma.f32 #s(literal 4 binary32) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32))) (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) #s(literal 12 binary32) (.f32 #s(literal 4 binary32) (sqrt.f32 (PI.f32))))) (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)) #s(literal -18 binary32) (fma.f32 #s(literal 4 binary32) (/.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (.f32 cosTheta cosTheta)) (.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -6 binary32))))) (.f32 cosTheta cosTheta))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
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(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* -4 (/ (* (PI) (- (* -1 (- c (sqrt (/ 1 (PI))))) 1)) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
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(* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal -3/2 binary32) (-.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 c (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal -3/2 binary32) (-.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 c (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) #s(literal -3/2 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32))))
(* (pow cosTheta 2) (+ (* -1 (/ (- (+ (* -1 (/ (- c (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) (/ 1 cosTheta)) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 cosTheta)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* -1 (- c (sqrt (/ 1 (PI))))) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta))))
(/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(+ 1 (+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(+ 1 (+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(+ 1 (+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
c
(* c (- (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(+.f32 c (.f32 c (-.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (/.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) c)) (/.f32 #s(literal 1 binary32) c))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
(* c (- (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(+.f32 c (.f32 c (-.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (/.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) c)) (/.f32 #s(literal 1 binary32) c))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
(* c (- (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (* cosTheta (- (* 1/2 cosTheta) 3/2)) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(+.f32 c (.f32 c (-.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (/.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) c)) (/.f32 #s(literal 1 binary32) c))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
c
(* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))
(neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c)))
(* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))
(neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c)))
(* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))
(neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (sqrt (/ 1 (PI))))) cosTheta)
(/.f32 (*.f32 (+.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* 1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2)))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2)))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt 2))))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 #s(literal 1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1)))))
(neg.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 #s(literal -1 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt -2)))))
(fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))) (neg.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 #s(literal -1 binary32))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt -2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt -2) 3))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -1 binary32)))) (fma.f32 (.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -2) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt -2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt -2) 3)))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -1 binary32)))) (fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (.f32 #s(literal -1/16 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))))))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (sqrt (PI))))))
(*.f32 cosTheta (fma.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* cosTheta (+ (sqrt (PI)) (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI)))))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3 binary32) (PI.f32))) (sqrt.f32 (PI.f32))) (neg.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* cosTheta (+ (sqrt (PI)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI))))) (* cosTheta (+ (* -1 (sqrt (PI))) (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (+ (* -4 (PI)) (* 8 (PI)))))))))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (fma.f32 cosTheta (fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (PI.f32) #s(literal 4 binary32) (PI.f32))) (neg.f32 (sqrt.f32 (PI.f32)))) (.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3 binary32) (PI.f32)))))) (neg.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* (sqrt (* cosTheta (PI))) (/ (sqrt 1/2) (exp (neg (pow cosTheta 2)))))
(/.f32 (.f32 (sqrt.f32 (.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal 1/2 binary32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (* (exp (neg (pow cosTheta 2))) (sqrt 1/2))))) (* (sqrt (/ (PI) cosTheta)) (/ (sqrt 1/2) (exp (neg (pow cosTheta 2)))))))
(.f32 cosTheta (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 #s(literal 1/2 binary32)))) (/.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) cosTheta)) (sqrt.f32 #s(literal 1/2 binary32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (* (exp (neg (pow cosTheta 2))) (sqrt 1/2))))) (+ (* 1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (* (exp (neg (pow cosTheta 2))) (sqrt 1/2))))) (* (sqrt (/ (PI) cosTheta)) (/ (sqrt 1/2) (exp (neg (pow cosTheta 2))))))))
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(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (+ (* 1/64 (/ (* cosTheta (PI)) (pow (sqrt 1/2) 2))) (* 1/16 (PI))) (* (exp (neg (pow cosTheta 2))) (sqrt 1/2))))) (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (* (exp (neg (pow cosTheta 2))) (sqrt 1/2))))) (+ (* 1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (* (exp (neg (pow cosTheta 2))) (sqrt 1/2))))) (* (sqrt (/ (PI) cosTheta)) (/ (sqrt 1/2) (exp (neg (pow cosTheta 2)))))))))
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(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (/ (* (sqrt -1) (sqrt -1/2)) (exp (neg (pow cosTheta 2)))))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (+ (* -1/64 (/ (* cosTheta (PI)) (pow (sqrt -1/2) 2))) (* 1/16 (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -1/2))))) (* 1/16 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (* (exp (neg (pow cosTheta 2))) (sqrt -1/2)))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (* (exp (neg (pow cosTheta 2))) (sqrt -1/2)))))))))
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(/ (+ 1 cosTheta) cosTheta)
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(/ (+ 1 (* cosTheta (+ 1 (* -3/2 cosTheta)))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal -3/2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) cosTheta)
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 (*.f32 cosTheta #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (.f32 #s(literal -1/2 binary32) (.f32 (+.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
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(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta)))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (fma.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (.f32 (.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32)))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))))))
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(neg.f32 (*.f32 cosTheta (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(neg.f32 (*.f32 cosTheta (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(neg.f32 (*.f32 cosTheta (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(*.f32 (neg.f32 cosTheta) (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(*.f32 (neg.f32 cosTheta) (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(*.f32 (neg.f32 cosTheta) (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))

eval135.0ms (1%)

Memory: 7.1MiB live, 329.5MiB allocated
Compiler: Compiled 36 290 to 4 360 computations (88% saved)

prune175.0ms (1.2%)

Memory

-41.5MiB live, 463.0MiB allocated

Pruning

41 alts after pruning (40 fresh and 1 done)

	Pruned	Kept	Total
New	1 042	29	1 071
Fresh	6	11	17
Picked	4	1	5
Done	0	0	0
Total	1 052	41	1 093

Accuracy

100.0%

Counts

1 093 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.4%	(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	52.5%	(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1/2 binary32))
	97.8%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
	49.3%	(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (*.f32 cosTheta cosTheta))))))))
▶	97.5%	(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
	97.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
▶	95.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	95.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
▶	52.9%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
	93.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	50.5%	(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	52.1%	(/.f32 #s(literal 1 binary32) (.f32 (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
	33.5%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta)))))
	52.2%	(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c))))
✓	4.9%	(/.f32 #s(literal 1 binary32) c)
▶	98.4%	(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	32.0%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
	52.2%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	93.5%	(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
▶	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	87.9%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1 binary32)))

Compiler

Compiled 2 161 to 1 204 computations (44.3% saved)

simplify419.0ms (2.9%)

Memory

41.1MiB live, 584.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
✓	cost-diff	0	(fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
✓	cost-diff	256	(fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32))
✓	cost-diff	0	(fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)
✓	cost-diff	0	(+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
✓	cost-diff	672	(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
✓	cost-diff	0	(-.f32 #s(literal 1 binary32) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	96	(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	192	(/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))
✓	cost-diff	0	(/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))
✓	cost-diff	0	(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
✓	cost-diff	672	(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))

Rules

17 000×	`lower-fma.f64`
16 980×	`lower-fma.f32`
4 008×	`lower-*.f64`
3 996×	`lower-*.f32`
3 632×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	622
0	90	619
1	165	619
2	370	617
3	1522	583
4	5680	583
0	8338	569

Stop Event

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

Calls

Call 1

Inputs
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))
cosTheta
(fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))
(*.f32 cosTheta cosTheta)
(pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(/.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
c
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
#s(literal -1 binary32)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
#s(literal 1 binary32)
#s(literal 3 binary32)
(fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
(*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
cosTheta
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
#s(literal 1 binary32)
(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(+.f32 #s(literal 1 binary32) c)
c
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
cosTheta
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(/.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
c
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
#s(literal -1 binary32)
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32))
c
(fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
#s(literal -2 binary32)
(PI.f32)
(*.f32 cosTheta c)

Outputs
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 (.f32 cosTheta (fma.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (.f32 cosTheta cosTheta))) (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))
cosTheta
(fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))
(fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))
(*.f32 cosTheta cosTheta)
(pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))
(pow.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(+.f32 c (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(/.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
c
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
#s(literal -1 binary32)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
#s(literal 1 binary32)
#s(literal 3 binary32)
(fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
(fma.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (*.f32 cosTheta cosTheta))
(*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(*.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)
(fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
cosTheta
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
#s(literal 1 binary32)
(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(+.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(-.f32 #s(literal 1 binary32) cosTheta)
cosTheta
(/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
c
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) cosTheta)))
cosTheta
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) cosTheta))
(+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(+.f32 c (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(/.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
c
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
#s(literal -1 binary32)
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(+.f32 cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32))))
#s(literal 1 binary32)
(fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32))
(+.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32)))
c
(fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta c)) #s(literal 1 binary32))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
#s(literal -2 binary32)
(PI.f32)
(*.f32 cosTheta c)

localize218.0ms (1.5%)

Memory

-7.1MiB live, 349.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.0%	(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
✓	accuracy	97.4%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	53.4%	(fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32))
✓	accuracy	99.0%	(/.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	98.2%	(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	95.8%	(*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
✓	accuracy	95.5%	(pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))

Samples

96.0ms

256×

valid

Compiler

Compiled 695 to 55 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-mult: 32.0ms (42.8% of total)

ival-div: 15.0ms (20.1% of total)

ival-add: 14.0ms (18.7% of total)

ival-sqrt: 4.0ms (5.3% of total)

ival-pow: 3.0ms (4% of total)

ival-exp: 2.0ms (2.7% of total)

ival-sub: 2.0ms (2.7% of total)

ival-pi: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

series163.0ms (1.1%)

Memory

4.4MiB live, 114.5MiB allocated

Counts

26 → 456

Calls

Call 1

Inputs
#<alt (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))>
#<alt (.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))>
#<alt (/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))>
#<alt (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))>
#<alt (*.f32 cosTheta (sqrt.f32 (PI.f32)))>
#<alt (sqrt.f32 (PI.f32))>
#<alt (PI.f32)>
#<alt (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)>
#<alt (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))>
#<alt (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))>
#<alt (-.f32 #s(literal 1 binary32) cosTheta)>
#<alt (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))>
#<alt (/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))>
#<alt (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))>
#<alt (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)>
#<alt (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32))>
#<alt (/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))>
#<alt (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32))>
#<alt (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))>
#<alt (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))>
#<alt (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))>
#<alt (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))>
#<alt (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))>
#<alt (/.f32 cosTheta (sqrt.f32 (PI.f32)))>
#<alt (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))>
#<alt (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c))>

Outputs
#<alt (sqrt (/ 1 (PI)))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI)))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))))>
#<alt (* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2))))))>
#<alt (* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))))))>
#<alt (* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))>
#<alt (* -1 (* (pow cosTheta 3) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* 3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>
#<alt (* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ c cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))>
#<alt (* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))>
#<alt (+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))>
#<alt (+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))>
#<alt (+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))>
#<alt (* c cosTheta)>
#<alt (* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))>
#<alt (* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))>
#<alt (* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))>
#<alt (* c cosTheta)>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* cosTheta (- (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* cosTheta (- (+ (* cosTheta (- (* (sqrt (pow (PI) 3)) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))) (* (pow (PI) 2) (+ 1 (+ (* -3 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI)))) (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))))) (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI)))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))>
#<alt (* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))>
#<alt (/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (* 2 (sqrt (PI)))) (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (+ (* 2 (sqrt (PI))) (* 8 (* (/ (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 9/4 (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (pow (PI) 3)))))) (+ (* 8 (* (/ (* (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))))))) (pow cosTheta 2)) (sqrt (pow (PI) 3)))) (+ (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* 16 (/ (* (pow (PI) 2) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* 9/4 (sqrt (/ 1 (pow (PI) 3))))))) (pow cosTheta 2)))))) (pow cosTheta 2))>
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Calls

114 calls:

Time	Variable		Point	Expression
30.0ms	c	@	0	(/ cosTheta (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (+ (/ 1 (sqrt (PI))) cosTheta)))
28.0ms	c	@	0	(* (/ cosTheta (+ (* cosTheta (* cosTheta cosTheta)) (pow (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) 3))) (+ (* cosTheta cosTheta) (* (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) (- (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) cosTheta))))
6.0ms	cosTheta	@	0	(+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (+ (/ 1 (sqrt (PI))) cosTheta))
4.0ms	cosTheta	@	inf	(* (/ cosTheta (+ (* cosTheta (* cosTheta cosTheta)) (pow (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) 3))) (+ (* cosTheta cosTheta) (* (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) (- (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) cosTheta))))
4.0ms	cosTheta	@	-inf	(* (/ cosTheta (+ (* cosTheta (* cosTheta cosTheta)) (pow (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) 3))) (+ (* cosTheta cosTheta) (* (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) (- (+ (* cosTheta (+ (+ (* (+ (* cosTheta 1/2) -3/2) (/ cosTheta (sqrt (PI)))) c) (/ -1 (sqrt (PI))))) (/ 1 (sqrt (PI)))) cosTheta))))

rewrite402.0ms (2.8%)

Memory

-4.2MiB live, 589.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 058×	`lower-*.f64`
4 046×	`lower-*.f32`
3 956×	`lower-fma.f64`
3 936×	`lower-fma.f32`
3 144×	`lower-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	440
0	90	437
1	409	422
2	3780	422
0	8151	422

Stop Event

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

Counts

26 → 752

Calls

Call 1

Inputs
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))
(fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(-.f32 #s(literal 1 binary32) cosTheta)
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)
(fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))
(*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(/.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c))

Outputs
(exp.f32 (log.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(+.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(+.f32 (*.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c)) (+.f32 (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(+.f32 (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c))) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(pow.f32 (/.f32 (-.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 cosTheta (sqrt.f32 (PI.f32))))) (+.f32 (/.f32 #s(literal -1 binary32) (*.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (pow.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (fma.f32 (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))
(fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (+.f32 (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) cosTheta (+.f32 (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(fma.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 #s(literal -1 binary32) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (*.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
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(pow.f32 (exp.f32 (log.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal 1/2 binary32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (neg.f32 (sqrt.f32 (PI.f32))))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(*.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))
(*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32)))))
(*.f32 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)) (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)))
(neg.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta (neg.f32 c))))
(neg.f32 (/.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (*.f32 cosTheta c)))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 cosTheta c) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (*.f32 cosTheta c) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 (*.f32 cosTheta c) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) #s(literal -1 binary32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (*.f32 cosTheta c) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 cosTheta c) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (*.f32 cosTheta c) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta c) (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (*.f32 cosTheta (neg.f32 c)))
(/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) c)
(/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta c)))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) (neg.f32 (*.f32 cosTheta (neg.f32 c))))
(/.f32 (neg.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)) (neg.f32 c))
(/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) c) cosTheta)
(/.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)) (.f32 cosTheta c))
(/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) (sqrt.f32 (PI.f32)))
(.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)))
(.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)))
(.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (neg.f32 c))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (pow.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (/.f32 c (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal -1 binary32)))
(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 #s(literal 1 binary32) c))
(*.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))
(.f32 (pow.f32 (/.f32 (.f32 cosTheta c) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))

simplify605.0ms (4.3%)

Memory

24.7MiB live, 1 062.9MiB allocated

Algorithm

1×	egg-herbie

Rules

6 844×	`lower-*.f64`
6 844×	`lower-*.f32`
6 066×	`lower-fma.f64`
6 066×	`lower-fma.f32`
4 538×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1919	26114
1	6588	25560
0	8121	23969

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 447

Calls

Call 1

Inputs
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))))
(* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2))))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))))))
(* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))
(* -1 (* (pow cosTheta 3) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* 3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ c cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))
(* c cosTheta)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* cosTheta (- (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* cosTheta (- (+ (* cosTheta (- (* (sqrt (pow (PI) 3)) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))) (* (pow (PI) 2) (+ 1 (+ (* -3 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI)))) (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))))) (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI)))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (* 2 (sqrt (PI)))) (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta))) (pow cosTheta 2))
(/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (+ (* 2 (sqrt (PI))) (* 8 (* (/ (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 9/4 (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (pow (PI) 3)))))) (+ (* 8 (* (/ (* (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))))))) (pow cosTheta 2)) (sqrt (pow (PI) 3)))) (+ (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* 16 (/ (* (pow (PI) 2) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* 9/4 (sqrt (/ 1 (pow (PI) 3))))))) (pow cosTheta 2)))))) (pow cosTheta 2))
(/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (+ (* 2 (sqrt (PI))) (+ (* 8 (* (/ (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (/ 1 (PI)))) (pow cosTheta 3)) (sqrt (pow (PI) 3)))) (* 8 (* (/ (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 9/4 (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (pow (PI) 3))))))) (+ (* 8 (* (/ (* (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))))))) (pow cosTheta 2)) (sqrt (pow (PI) 3)))) (+ (* 8 (* (/ (* (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) (- (* 8 (* (sqrt (pow (PI) 3)) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 9/4 (/ 1 (PI))))))) (+ (* 8 (* (sqrt (pow (PI) 3)) (* (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))))))))) (* 16 (* (pow (PI) 2) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* 9/4 (sqrt (/ 1 (pow (PI) 3))))))))))) (pow cosTheta 3)) (sqrt (pow (PI) 3)))) (+ (* 8 (* (/ (* (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* 9/4 (sqrt (/ 1 (pow (PI) 3)))))) (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))))))) (pow cosTheta 3)) (sqrt (pow (PI) 3)))) (+ (* 16 (/ (* (pow (PI) 2) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/4 (sqrt (/ 1 (pow (PI) 3)))) (* 1/2 (* (sqrt (/ 1 (PI))) (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))))))))) (pow cosTheta 3))) (+ (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* 16 (/ (* (pow (PI) 2) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* 9/4 (sqrt (/ 1 (pow (PI) 3))))))) (pow cosTheta 2))))))))) (pow cosTheta 2))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (* 2 (sqrt (PI)))) (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- (+ (* -8 (* (/ (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (* 9/4 (/ 1 (PI))))) cosTheta) (sqrt (pow (PI) 3)))) (* -1 (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))))))) (+ (* -8 (* (/ (* (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) (- (* -12 (sqrt (PI))) (* 16 (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))))))) cosTheta) (sqrt (pow (PI) 3)))) (* 16 (/ (* (pow (PI) 2) (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI)))))) cosTheta)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
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(* (pow c 3) (pow cosTheta 3))
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c
(* c (+ 1 (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) c)) 1)))
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(/ 1 c)
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(/ 1 c)
(* -1 (/ (- (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2) c) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
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1
(+ 1 (* -1 cosTheta))
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(* -1 (* cosTheta (- 1 (/ 1 cosTheta))))
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(sqrt (/ 1 (PI)))
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(* -1 (* (pow cosTheta 3) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* 3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
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(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (- (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))) 1) cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
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(+ cosTheta (+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (+ (/ cosTheta c) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c)))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (+ (/ cosTheta c) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c)))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (+ (/ cosTheta c) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c)))))
(* c cosTheta)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c)))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (pow cosTheta 2)))))) (pow cosTheta 2))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* -4 (/ (* (PI) (- (* -1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 1)) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
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(* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))
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(* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
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(/ (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)
(/ (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)
1
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1
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1
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(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
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(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(sqrt (/ 1 (pow (PI) 3)))
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(* (pow cosTheta 9) (+ (* -3/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 3) (PI)))) (+ (* -3/4 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* -3/8 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/8 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 1/4 (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 2) (PI)))) (+ (* 1/2 (* (/ (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 9/4 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (pow (PI) 3)))))))))))))))
(* 1/8 (* (pow cosTheta 9) (sqrt (/ 1 (pow (PI) 3)))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -1 (/ (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))))) cosTheta)) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -1 (/ (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1 (/ (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (- (* 3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))))) (* 1/4 (sqrt (/ 1 (pow (PI) 3))))))) cosTheta)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI)))))) cosTheta)) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3)
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(* (pow c 3) (pow cosTheta 3))
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(* (pow c 3) (pow cosTheta 3))
(* -1 (* (pow c 3) (+ (* -1 (/ (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) c)) (* -1 (pow cosTheta 3)))))
(* -1 (* (pow c 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (* -1 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)))) c)) (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))))) c)) (* -1 (pow cosTheta 3)))))
(* -1 (* (pow c 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (+ (* -1 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (* -1 (/ (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3) c)))) c)) (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))))) c)) (* -1 (pow cosTheta 3)))))
(/ 1 (PI))
(+ (* cosTheta (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (/ 1 (PI)))
(+ (* cosTheta (+ (* cosTheta (- (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)) (* 3 (/ 1 (PI))))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (/ 1 (PI)))
(+ (* cosTheta (+ (* cosTheta (- (+ (* cosTheta (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (/ 1 (PI))))) (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (/ 1 (PI)))
(* 1/4 (/ (pow cosTheta 6) (PI)))
(* (pow cosTheta 6) (- (* 1/4 (/ 1 (PI))) (* 3/2 (/ 1 (* cosTheta (PI))))))
(* (pow cosTheta 6) (- (+ (* 1/2 (* (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/4 (/ 1 (PI))) (* 9/4 (/ 1 (* (pow cosTheta 2) (PI))))))) (/ 3/2 (* cosTheta (PI)))))
(* (pow cosTheta 6) (- (+ (* -3/2 (* (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* -3/2 (* (/ (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/4 (/ 1 (PI))) (+ (* 9/4 (/ 1 (* (pow cosTheta 2) (PI)))) (/ 1 (* (pow cosTheta 3) (PI))))))))) (/ 3/2 (* cosTheta (PI)))))
(* 1/4 (/ (pow cosTheta 6) (PI)))
(* (pow cosTheta 6) (- (* 1/4 (/ 1 (PI))) (* 3/2 (/ 1 (* cosTheta (PI))))))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (* 9/4 (/ 1 (PI))))) cosTheta)) (* 3/2 (/ 1 (PI)))) cosTheta)) (* 1/4 (/ 1 (PI)))))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (* 3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))))) (/ 1 (PI))) cosTheta)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (* 9/4 (/ 1 (PI)))))) cosTheta)) (* 3/2 (/ 1 (PI)))) cosTheta)) (* 1/4 (/ 1 (PI)))))
(* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))
(+ (* c (+ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))) (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))
(+ (* c (+ (* c (pow cosTheta 2)) (+ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))))) (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))
(+ (* c (+ (* c (pow cosTheta 2)) (+ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))))) (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))
(* (pow c 2) (pow cosTheta 2))
(* (pow c 2) (+ (/ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c) (pow cosTheta 2))))
(* (pow c 2) (+ (/ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c) (+ (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) (pow c 2)) (pow cosTheta 2)))))
(* (pow c 2) (+ (/ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c) (+ (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) (pow c 2)) (pow cosTheta 2)))))
(* (pow c 2) (pow cosTheta 2))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))) c)) (pow cosTheta 2)))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (+ (* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))) (* -1 (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c)))) c)) (pow cosTheta 2)))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (+ (* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))) (* -1 (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c)))) c)) (pow cosTheta 2)))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (/ 1 (PI))))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))
(/ (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ cosTheta c) (sqrt (/ 1 (PI))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ cosTheta c) (sqrt (/ 1 (PI))))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI)))))
(+ (* 1/2 (* (/ 1 (* c (sqrt -2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI))))))
(+ (* -1/8 (* (/ 1 (* c (pow (sqrt -2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))) (+ (* 1/2 (* (/ 1 (* c (sqrt -2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI)))))))
(+ (* -1/8 (* (/ 1 (* c (pow (sqrt -2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))) (+ (* 1/16 (* (/ 1 (* c (pow (sqrt -2) 5))) (sqrt (/ 1 (* (pow cosTheta 7) (PI)))))) (+ (* 1/2 (* (/ 1 (* c (sqrt -2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI))))))))
(* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI))))))
(+ (* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI)))))) (* -1/2 (* (/ (sqrt -1) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))))
(+ (* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (sqrt -1) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* 1/8 (* (/ (sqrt -1) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI))))))))
(+ (* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (sqrt -1) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (+ (* -1/16 (* (/ (sqrt -1) (* c (pow (sqrt 2) 5))) (sqrt (/ 1 (* (pow cosTheta 7) (PI)))))) (* 1/8 (* (/ (sqrt -1) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))

Outputs
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI)))))))
(fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (fma.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))))
(fma.f32 cosTheta (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (.f32 (*.f32 #s(literal -3/2 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2))))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 #s(literal -3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)) (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 c (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(* (pow cosTheta 3) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 #s(literal -3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)) (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (/.f32 c (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(* 1/2 (* (pow cosTheta 3) (sqrt (/ 1 (PI)))))
(.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* -1 (* (pow cosTheta 3) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* 3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32) (.f32 (*.f32 #s(literal 3/2 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ c cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
(neg.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (-.f32 (/.f32 c cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta))))
(* -1 (* (pow cosTheta 3) (+ (* -1 (/ (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)) (* -1/2 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (/.f32 (-.f32 (neg.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) cosTheta)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))
(fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (*.f32 cosTheta c)))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (*.f32 cosTheta c)))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (*.f32 cosTheta c)))
(* c cosTheta)
(*.f32 cosTheta c)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))
(.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))
(.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))))
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))) c))))
(.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))))
(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))
(neg.f32 (.f32 c (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))
(neg.f32 (.f32 c (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) c)))))
(neg.f32 (.f32 c (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* cosTheta (- (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* cosTheta (- (+ (* cosTheta (- (* (sqrt (pow (PI) 3)) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))) (* (pow (PI) 2) (+ 1 (+ (* -3 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI)))) (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))))) (* (sqrt (pow (PI) 3)) (- (+ 1 (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI)))))) (+ (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (- (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1)))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))) (* (pow (PI) 2) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (sqrt (pow (PI) 3)) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (* (pow (PI) 2) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
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(/ (- (+ (* -12 (* (/ 1 cosTheta) (sqrt (PI)))) (* 2 (sqrt (PI)))) (* 16 (/ (* (pow (PI) 2) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta))) (pow cosTheta 2))
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cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta cosTheta))) (/.f32 (.f32 (.f32 #s(literal 3 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (-.f32 (neg.f32 (/.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta (+.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 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(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)) #s(literal -1 binary32)) c))
(* cosTheta (sqrt (pow (PI) 3)))
(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))))
(* cosTheta (+ (sqrt (pow (PI) 3)) (* -1 (* cosTheta (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
(.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))
(* cosTheta (+ (sqrt (pow (PI) 3)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 9)) (pow (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) 2))) (* (pow (PI) 3) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32))))))) (neg.f32 (.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 9 binary32))) (.f32 (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))))) (neg.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))) (sqrt.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))
(* cosTheta (+ (sqrt (pow (PI) 3)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) (+ (* -1 (* (sqrt (pow (PI) 9)) (pow (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) 2))) (* (pow (PI) 3) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))) (+ (* -1 (* (sqrt (pow (PI) 9)) (* (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI))))))) (* (pow (PI) 3) (+ 1 (+ (* -3 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* 1/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI)))) (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI)))))))))))))) (+ (* -1 (* (sqrt (pow (PI) 9)) (pow (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))) 2))) (* (pow (PI) 3) (+ (* -3/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (- (pow (+ c (* -1 (sqrt (/ 1 (PI))))) 2) (* 3 (/ 1 (PI))))))))))) (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ c (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (-.f32 (-.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) #s(literal -3 binary32) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (.f32 #s(literal -3 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32)))))))))) (.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 9 binary32))) (.f32 (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32)))))))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32))))))) (neg.f32 (.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 9 binary32))) (.f32 (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))))))) (neg.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32))))))) (neg.f32 (.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 9 binary32))) (.f32 (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))))))) (neg.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))
(* 8 (* (/ 1 (pow cosTheta 8)) (sqrt (pow (PI) 3))))
(.f32 #s(literal 8 binary32) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 8 binary32)))))
(/ (+ (* -64 (/ (* (pow (PI) 3) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* 8 (sqrt (pow (PI) 3)))) (pow cosTheta 8))
(/.f32 (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) #s(literal 8 binary32) (/.f32 (.f32 (.f32 #s(literal -64 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) #s(literal -9/8 binary32))) cosTheta)) (pow.f32 cosTheta #s(literal 8 binary32)))
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(fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (fma.f32 cosTheta (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) #s(literal -3 binary32) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (.f32 #s(literal -3 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32))))))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32)))))))) (/.f32 c (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))
(* 1/8 (* (pow cosTheta 9) (sqrt (/ 1 (pow (PI) 3)))))
(.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 cosTheta #s(literal 9 binary32))))
(* (pow cosTheta 9) (+ (* -3/4 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* -3/8 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (* 1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (fma.f32 #s(literal -3/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/8 binary32) (.f32 (.f32 #s(literal -3/8 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))))
(* (pow cosTheta 9) (+ (* -3/4 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* -3/8 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/8 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 2) (PI)))) (+ (* 1/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 9/4 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (pow (PI) 3)))))))))))
(.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (fma.f32 #s(literal -3/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal -3/8 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/8 binary32) (fma.f32 #s(literal 1/4 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (.f32 cosTheta cosTheta)) (.f32 (.f32 #s(literal 9/4 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))))))
(* (pow cosTheta 9) (+ (* -3/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 3) (PI)))) (+ (* -3/4 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* -3/8 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/8 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 1/4 (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 2) (PI)))) (+ (* 1/2 (* (/ (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 9/4 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (pow (PI) 3)))))))))))))))
(.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (fma.f32 #s(literal -3/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (fma.f32 #s(literal -3/2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 #s(literal -3/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal -3/8 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/8 binary32) (fma.f32 #s(literal 1/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (.f32 #s(literal -3 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (.f32 cosTheta cosTheta)) (.f32 (.f32 #s(literal 9/4 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))))))))))
(* 1/8 (* (pow cosTheta 9) (sqrt (/ 1 (pow (PI) 3)))))
(.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 cosTheta #s(literal 9 binary32))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(neg.f32 (.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -1/8 binary32)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) #s(literal -9/8 binary32)) cosTheta))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -1 (/ (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))))) cosTheta)) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(neg.f32 (.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -1/8 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -9/8 binary32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -9/4 binary32) (fma.f32 (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) #s(literal -1/4 binary32) (.f32 #s(literal -1/2 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32))))))) cosTheta)) cosTheta))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -1 (/ (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1 (/ (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (- (* 3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))))) (* 1/4 (sqrt (/ 1 (pow (PI) 3))))))) cosTheta)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI)))))) cosTheta)) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(neg.f32 (.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -1/8 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -9/8 binary32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -9/4 binary32) (-.f32 (fma.f32 (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) #s(literal -1/4 binary32) (.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))))) (/.f32 (fma.f32 #s(literal -3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (fma.f32 #s(literal -3/2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)) (fma.f32 (.f32 #s(literal 3 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) #s(literal 1/4 binary32))))) cosTheta))) cosTheta)) cosTheta))))
(+ (pow cosTheta 3) (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3))
(fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32)))
(+ (* c (+ (* 2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)))) (+ (pow cosTheta 3) (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3)))
(fma.f32 c (.f32 #s(literal 3 binary32) (.f32 cosTheta (.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))))
(+ (* c (+ (* 2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (+ (* c (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))))) (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))))) (+ (pow cosTheta 3) (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3)))
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(+ (* c (+ (* 2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (+ (* c (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (+ (* c (pow cosTheta 3)) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))))) (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))))) (+ (pow cosTheta 3) (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3)))
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(* (pow c 3) (pow cosTheta 3))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 c (*.f32 c c)))
(* (pow c 3) (+ (* 2 (/ (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c)) (+ (/ (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (pow cosTheta 3))))
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(* (pow c 3) (+ (* 2 (/ (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)) (pow c 2))) (+ (* 2 (/ (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c)) (+ (/ (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)) (pow c 2)) (+ (/ (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (pow cosTheta 3))))))
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(* (pow c 3) (+ (* 2 (/ (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)) (pow c 2))) (+ (* 2 (/ (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c)) (+ (/ (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)) (pow c 2)) (+ (/ (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (pow cosTheta 3) (pow c 3)) (+ (/ (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3) (pow c 3)) (pow cosTheta 3))))))))
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(* (pow c 3) (pow cosTheta 3))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 c (*.f32 c c)))
(* -1 (* (pow c 3) (+ (* -1 (/ (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) c)) (* -1 (pow cosTheta 3)))))
(neg.f32 (.f32 (.f32 c (.f32 c c)) (-.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (/.f32 (.f32 #s(literal 3 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) c))))
(* -1 (* (pow c 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (* -1 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2)))) c)) (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))))) c)) (* -1 (pow cosTheta 3)))))
(neg.f32 (.f32 (.f32 c (.f32 c c)) (-.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (.f32 #s(literal 3 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 (.f32 (.f32 cosTheta (.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) #s(literal -3 binary32)) c)) c))))
(* -1 (* (pow c 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -2 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (+ (* -1 (* cosTheta (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 2))) (* -1 (/ (+ (pow cosTheta 3) (pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3)) c)))) c)) (+ (* 2 (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* (pow cosTheta 2) (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))))) c)) (* -1 (pow cosTheta 3)))))
(neg.f32 (.f32 (.f32 c (.f32 c c)) (-.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (.f32 #s(literal 3 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 (-.f32 (.f32 (.f32 cosTheta (.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) #s(literal -3 binary32)) (/.f32 (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))) c)) c)) c))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
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(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))) 2))) (* c (* (PI) (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))))))) (* (PI) (+ 1 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))))))
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(* 1/8 (* (pow cosTheta 9) (sqrt (/ 1 (pow (PI) 3)))))
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(* (pow cosTheta 9) (+ (* -3/4 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* -3/8 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/8 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 2) (PI)))) (+ (* 1/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 9/4 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (pow (PI) 3)))))))))))
(.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (fma.f32 #s(literal -3/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal -3/8 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/8 binary32) (fma.f32 #s(literal 1/4 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (.f32 cosTheta cosTheta)) (.f32 (.f32 #s(literal 9/4 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))))))
(* (pow cosTheta 9) (+ (* -3/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 3) (PI)))) (+ (* -3/4 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* -3/8 (* (/ 1 cosTheta) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/8 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 1/4 (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (pow (PI) 3))))) (+ (* 1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (* (pow cosTheta 2) (PI)))) (+ (* 1/2 (* (/ (+ (* -3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 9/4 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (pow (PI) 3)))))))))))))))
(.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (fma.f32 #s(literal -3/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (fma.f32 #s(literal -3/2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 #s(literal -3/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal -3/8 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1/8 binary32) (fma.f32 #s(literal 1/4 binary32) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (.f32 #s(literal -3 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (.f32 cosTheta cosTheta)) (.f32 (.f32 #s(literal 9/4 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))))))))))))))
(* 1/8 (* (pow cosTheta 9) (sqrt (/ 1 (pow (PI) 3)))))
(.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 cosTheta #s(literal 9 binary32))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
(neg.f32 (.f32 (pow.f32 cosTheta #s(literal 9 binary32)) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) #s(literal -1/8 binary32)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) #s(literal -9/8 binary32)) cosTheta))))
(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -1 (/ (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))))) cosTheta)) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
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(* -1 (* (pow cosTheta 9) (+ (* -1 (/ (+ (* -1 (/ (+ (* -9/4 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1 (/ (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (+ (* -3/2 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI))) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (- (* 3 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (/ 1 (PI))))) (* 1/4 (sqrt (/ 1 (pow (PI) 3))))))) cosTheta)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* 9/4 (/ 1 (PI)))))) (* -1/4 (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (PI)))))) cosTheta)) (+ (* -3/4 (sqrt (/ 1 (pow (PI) 3)))) (* -3/8 (sqrt (/ 1 (pow (PI) 3)))))) cosTheta)) (* -1/8 (sqrt (/ 1 (pow (PI) 3)))))))
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(pow (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) 3)
(pow.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))
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(* (pow c 3) (pow cosTheta 3))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 c (*.f32 c c)))
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(/ 1 (PI))
(/.f32 #s(literal 1 binary32) (PI.f32))
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(fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32))) (*.f32 cosTheta (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32)) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32)))))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (* cosTheta (+ (* cosTheta (- (+ (* cosTheta (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (+ (* -3/2 (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (/ 1 (PI))))) (* (+ c (* -1 (sqrt (/ 1 (PI))))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))) (* 3 (/ 1 (PI))))) (+ (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1))))) (/ 1 (PI)))
(fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32)) (neg.f32 (/.f32 #s(literal 3 binary32) (PI.f32))))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(* 1/4 (/ (pow cosTheta 6) (PI)))
(*.f32 #s(literal 1/4 binary32) (/.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)))
(* (pow cosTheta 6) (- (* 1/4 (/ 1 (PI))) (* 3/2 (/ 1 (* cosTheta (PI))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (-.f32 (/.f32 #s(literal 1/4 binary32) (PI.f32)) (/.f32 #s(literal 3/2 binary32) (.f32 (PI.f32) cosTheta))))
(* (pow cosTheta 6) (- (+ (* 1/2 (* (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/4 (/ 1 (PI))) (* 9/4 (/ 1 (* (pow cosTheta 2) (PI))))))) (/ 3/2 (* cosTheta (PI)))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta cosTheta)) (-.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32))) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1/4 binary32) (PI.f32)) (/.f32 #s(literal 9/4 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal 3/2 binary32) (.f32 (PI.f32) cosTheta)))))
(* (pow cosTheta 6) (- (+ (* -3/2 (* (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* -3/2 (* (/ (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1) (pow cosTheta 3)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (+ c (* -1 (sqrt (/ 1 (PI))))) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (* (/ (- (+ c (* -1 (sqrt (/ 1 (PI))))) 1) (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/4 (/ 1 (PI))) (+ (* 9/4 (/ 1 (* (pow cosTheta 2) (PI)))) (/ 1 (* (pow cosTheta 3) (PI))))))))) (/ 3/2 (* cosTheta (PI)))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (fma.f32 #s(literal -3/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (-.f32 (fma.f32 #s(literal -3/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta cosTheta)) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32))) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1/4 binary32) (PI.f32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 9/4 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))))) (/.f32 #s(literal 3/2 binary32) (*.f32 (PI.f32) cosTheta)))))
(* 1/4 (/ (pow cosTheta 6) (PI)))
(*.f32 #s(literal 1/4 binary32) (/.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)))
(* (pow cosTheta 6) (- (* 1/4 (/ 1 (PI))) (* 3/2 (/ 1 (* cosTheta (PI))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (-.f32 (/.f32 #s(literal 1/4 binary32) (PI.f32)) (/.f32 #s(literal 3/2 binary32) (.f32 (PI.f32) cosTheta))))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (* 9/4 (/ 1 (PI))))) cosTheta)) (* 3/2 (/ 1 (PI)))) cosTheta)) (* 1/4 (/ 1 (PI)))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (-.f32 (/.f32 #s(literal 1/4 binary32) (PI.f32)) (/.f32 (-.f32 (/.f32 #s(literal 3/2 binary32) (PI.f32)) (/.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) cosTheta)) cosTheta)))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (* 3/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI)))))))) (/ 1 (PI))) cosTheta)) (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ 1 (* -1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 1/2 (* (sqrt (/ 1 (PI))) (+ c (* -1 (sqrt (/ 1 (PI))))))) (* 9/4 (/ 1 (PI)))))) cosTheta)) (* 3/2 (/ 1 (PI)))) cosTheta)) (* 1/4 (/ 1 (PI)))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (-.f32 (/.f32 #s(literal 1/4 binary32) (PI.f32)) (/.f32 (-.f32 (/.f32 #s(literal 3/2 binary32) (PI.f32)) (/.f32 (-.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 9/4 binary32) (PI.f32)))) (/.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) cosTheta)) cosTheta)))
(* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))
(.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(+ (* c (+ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))) (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))
(fma.f32 c (.f32 cosTheta (+.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) (.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(+ (* c (+ (* c (pow cosTheta 2)) (+ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))))) (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))
(fma.f32 c (fma.f32 cosTheta (+.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) (.f32 c (.f32 cosTheta cosTheta))) (.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(+ (* c (+ (* c (pow cosTheta 2)) (+ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))))) (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))
(fma.f32 c (fma.f32 cosTheta (+.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) (.f32 c (.f32 cosTheta cosTheta))) (.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(* (pow c 2) (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) (*.f32 c c))
(* (pow c 2) (+ (/ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c) (pow cosTheta 2))))
(.f32 (.f32 c c) (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (fma.f32 cosTheta (/.f32 (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) c) (*.f32 cosTheta cosTheta))))
(* (pow c 2) (+ (/ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c) (+ (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) (pow c 2)) (pow cosTheta 2)))))
(.f32 (.f32 c c) (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (fma.f32 cosTheta (/.f32 (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) c) (fma.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (.f32 c c)) (.f32 cosTheta cosTheta)))))
(* (pow c 2) (+ (/ (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))))))) c) (+ (/ (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c) (+ (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) (pow c 2)) (pow cosTheta 2)))))
(.f32 (.f32 c c) (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (fma.f32 cosTheta (/.f32 (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) c) (fma.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (.f32 c c)) (.f32 cosTheta cosTheta)))))
(* (pow c 2) (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) (*.f32 c c))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)))) c)) (pow cosTheta 2)))
(.f32 (.f32 c c) (-.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta (+.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))) c)))
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (+ (* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))) (* -1 (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c)))) c)) (pow cosTheta 2)))
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(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))))) (+ (* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta))) (* -1 (/ (* (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) (- (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI))))))) cosTheta)) c)))) c)) (pow cosTheta 2)))
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(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* cosTheta (sqrt (/ 1 (PI))))
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(* cosTheta (sqrt (/ 1 (PI))))
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(* cosTheta (sqrt (/ 1 (PI))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 cosTheta (PI.f32)))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
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(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(.f32 (neg.f32 cosTheta) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
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(* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))
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(/ (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 cosTheta c))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ cosTheta c) (sqrt (/ 1 (PI))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 cosTheta c)) (neg.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ cosTheta c) (sqrt (/ 1 (PI))))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (fma.f32 cosTheta (.f32 #s(literal -1/2 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 cosTheta c)))) (neg.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)))))) cosTheta)
(* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI)))))
(/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)))) c)
(+ (* 1/2 (* (/ 1 (* c (sqrt -2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI))))))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 c (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)))) c))
(+ (* -1/8 (* (/ 1 (* c (pow (sqrt -2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))) (+ (* 1/2 (* (/ 1 (* c (sqrt -2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI)))))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 c (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 c (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) cosTheta)))) c)))
(+ (* -1/8 (* (/ 1 (* c (pow (sqrt -2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))) (+ (* 1/16 (* (/ 1 (* c (pow (sqrt -2) 5))) (sqrt (/ 1 (* (pow cosTheta 7) (PI)))))) (+ (* 1/2 (* (/ 1 (* c (sqrt -2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* (/ (sqrt -2) c) (sqrt (/ 1 (* cosTheta (PI))))))))
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(* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI))))))
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(+ (* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI)))))) (* -1/2 (* (/ (sqrt -1) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 c (sqrt.f32 #s(literal 2 binary32)))) (neg.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (/.f32 (sqrt.f32 #s(literal 2 binary32)) c)))))
(+ (* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (sqrt -1) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* 1/8 (* (/ (sqrt -1) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI))))))))
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(+ (* -1 (* (/ (* (sqrt -1) (sqrt 2)) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (sqrt -1) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (+ (* -1/16 (* (/ (sqrt -1) (* c (pow (sqrt 2) 5))) (sqrt (/ 1 (* (pow cosTheta 7) (PI)))))) (* 1/8 (* (/ (sqrt -1) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))))))
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(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(* (/ 1 (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))

eval784.0ms (5.5%)

Memory: -132.6MiB live, 1 194.2MiB allocated
Compiler: Compiled 200 110 to 10 619 computations (94.7% saved)

prune416.0ms (2.9%)

Memory

9.7MiB live, 923.8MiB allocated

Pruning

36 alts after pruning (33 fresh and 3 done)

	Pruned	Kept	Total
New	2 791	18	2 809
Fresh	20	15	35
Picked	3	2	5
Done	0	1	1
Total	2 814	36	2 850

Accuracy

100.0%

Counts

2 850 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.5%	(/.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) c) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
▶	95.7%	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
	97.5%	(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
	97.5%	(/.f32 cosTheta (+.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
	96.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
✓	95.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	95.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
▶	95.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
▶	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	52.9%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	52.8%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	52.3%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	50.7%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	50.5%	(/.f32 #s(literal 1 binary32) (fma.f32 c (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c))))) cosTheta) #s(literal 1 binary32)))
	47.8%	(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	93.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
▶	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
	93.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
✓	4.9%	(/.f32 #s(literal 1 binary32) c)
	93.6%	(.f32 (/.f32 cosTheta (fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (fma.f32 cosTheta cosTheta (.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	32.0%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
	52.2%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	93.5%	(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
	94.1%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 586 to 926 computations (41.6% saved)

simplify488.0ms (3.4%)

Memory

-5.0MiB live, 686.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
✓	cost-diff	64	(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
✓	cost-diff	672	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	cost-diff	0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	0	(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	0	(fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
✓	cost-diff	0	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (PI.f32))
✓	cost-diff	0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	0	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	cost-diff	0	(*.f32 cosTheta (neg.f32 cosTheta))
✓	cost-diff	0	(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
✓	cost-diff	0	(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))

Rules

19 838×	`lower-fma.f64`
19 824×	`lower-fma.f32`
3 230×	`lower-+.f64`
3 222×	`lower-+.f32`
2 466×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	304
0	78	300
1	136	291
2	283	291
3	630	291
4	1775	291
5	3901	291
6	6278	291
0	8005	289

Stop Event

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

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
#s(literal -2 binary32)
(PI.f32)
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
cosTheta
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) cosTheta)
cosTheta
#s(literal -1 binary32)
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
cosTheta
(fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 1 binary32)
(PI.f32)
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(+.f32 #s(literal 1 binary32) c)
c
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))
cosTheta
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(/.f32 #s(literal 1 binary32) cosTheta)
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))

Outputs
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 cosTheta (neg.f32 cosTheta))
cosTheta
(neg.f32 cosTheta)
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
#s(literal -2 binary32)
(PI.f32)
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
cosTheta
(sqrt.f32 (PI.f32))
(PI.f32)
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) cosTheta)
cosTheta
#s(literal -1 binary32)
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
cosTheta
(fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
#s(literal 1 binary32)
(PI.f32)
(+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(+.f32 cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c)))
#s(literal 1 binary32)
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c))
(+.f32 #s(literal 1 binary32) c)
c
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(PI.f32)
(fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))
cosTheta
(fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))
#s(literal 1/2 binary32)
#s(literal -3/2 binary32)
(/.f32 #s(literal 1 binary32) cosTheta)
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))

localize259.0ms (1.8%)

Memory

-22.5MiB live, 220.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
✓	accuracy	98.2%	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.7%	(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	98.3%	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
✓	accuracy	98.1%	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
✓	accuracy	98.3%	(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
✓	accuracy	97.4%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))

Samples

134.0ms

256×

valid

Compiler

Compiled 330 to 48 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-add: 47.0ms (46.8% of total)

ival-mult: 21.0ms (20.9% of total)

ival-div: 20.0ms (19.9% of total)

ival-sqrt: 5.0ms (5% of total)

ival-neg: 3.0ms (3% of total)

ival-exp: 2.0ms (2% of total)

ival-pi: 1.0ms (1% of total)

ival-sub: 1.0ms (1% of total)

exact: 1.0ms (1% of total)

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

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

series134.0ms (0.9%)

Memory

1.3MiB live, 79.5MiB allocated

Counts

26 → 300

Calls

Call 1

Inputs
#<alt (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))>
#<alt (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))>
#<alt (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))>
#<alt (*.f32 cosTheta (neg.f32 cosTheta))>
#<alt (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))>
#<alt (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))>
#<alt (*.f32 cosTheta (sqrt.f32 (PI.f32)))>
#<alt (sqrt.f32 (PI.f32))>
#<alt (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))>
#<alt (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))>
#<alt (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))>
#<alt (/.f32 #s(literal 1 binary32) (PI.f32))>
#<alt (/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))>
#<alt (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))>
#<alt (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))>
#<alt (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))>
#<alt (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))>
#<alt (+.f32 #s(literal 1 binary32) c)>
#<alt (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))>
#<alt (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)>
#<alt (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))>
#<alt (PI.f32)>
#<alt (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))>
#<alt (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))>
#<alt (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))>

Outputs
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))>
#<alt (- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))))>
#<alt (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))>
#<alt (- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))))>
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#<alt c>
#<alt (* c (- (+ 1 (+ (* (/ (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)) c) (sqrt (/ 1 (PI)))) (/ 1 c))) (* (/ 1 c) (sqrt (/ 1 (PI))))))>
#<alt (* c (- (+ 1 (+ (* (/ (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)) c) (sqrt (/ 1 (PI)))) (/ 1 c))) (* (/ 1 c) (sqrt (/ 1 (PI))))))>
#<alt (* c (- (+ 1 (+ (* (/ (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)) c) (sqrt (/ 1 (PI)))) (/ 1 c))) (* (/ 1 c) (sqrt (/ 1 (PI))))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) c)) 1)))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))) (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))>
#<alt (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (- (+ 1 c) (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (- (+ 1 (+ c (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (/ 1 (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (/ c (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 2))) (/ 1 (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))))>
#<alt (+ (* c (- (/ c (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 3)) (/ 1 (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 2)))) (/ 1 (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))))>
#<alt (+ (* c (- (* c (+ (* -1 (/ c (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 4))) (/ 1 (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 3)))) (/ 1 (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 2)))) (/ 1 (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))))>
#<alt (/ 1 c)>
#<alt (/ (- (+ 1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* (/ (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)) c) (sqrt (/ 1 (PI)))) (/ 1 c))) c)>
#<alt (/ (- (+ 1 (+ (* -1 (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))) (pow c 2))) (* (/ 1 c) (sqrt (/ 1 (PI)))))) (+ (* (/ (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)) c) (sqrt (/ 1 (PI)))) (/ 1 c))) c)>
#<alt (/ (- (+ 1 (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 2)) (pow c 3)))) (+ (* (/ (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)) c) (sqrt (/ 1 (PI)))) (+ (/ 1 c) (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))) (pow c 2))))) c)>
#<alt (/ 1 c)>
#<alt (* -1 (/ (- (* -1 (/ (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) c)) 1) c))>
#<alt (* -1 (/ (- (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))) c))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) c)) 1) c))>
#<alt (* -1 (/ (- (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (/ (- (* -1 (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 2)) c)) (* -1 (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))))) c))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) c)) 1) c))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))>
#<alt (* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))>
#<alt (/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) (pow cosTheta 2)))))) (pow cosTheta 2))>
#<alt (* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))>
#<alt (/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) cosTheta)) (+ (* -4 (* (/ 1 cosTheta) (sqrt (PI)))) (* -3 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))))) cosTheta)))) (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) cosTheta)) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))>
#<alt 1>
#<alt (+ 1 c)>
#<alt (+ 1 c)>
#<alt (+ 1 c)>
#<alt c>
#<alt (* c (+ 1 (/ 1 c)))>
#<alt (* c (+ 1 (/ 1 c)))>
#<alt (* c (+ 1 (/ 1 c)))>
#<alt c>
#<alt (* c (+ 1 (/ 1 c)))>
#<alt (* c (+ 1 (/ 1 c)))>
#<alt (* c (+ 1 (/ 1 c)))>
#<alt (sqrt (/ 1 (PI)))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))>
#<alt (* (sqrt (/ cosTheta (PI))) (sqrt -2))>
#<alt (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))>
#<alt (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))>
#<alt (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))>
#<alt (* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))>
#<alt (* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))>
#<alt (* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))>
#<alt (* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)>
#<alt (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))>
#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))>
#<alt (/ 1 (PI))>
#<alt (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))>
#<alt (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))>
#<alt (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))>
#<alt (* -2 (/ cosTheta (PI)))>
#<alt (* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))>
#<alt (* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))>
#<alt (* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))>
#<alt (* -2 (/ cosTheta (PI)))>
#<alt (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))>
#<alt (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))>
#<alt (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))>
#<alt (/ 1 cosTheta)>
#<alt (/ (+ 1 (* -1 cosTheta)) cosTheta)>
#<alt (/ (+ 1 (* -1 cosTheta)) cosTheta)>
#<alt (/ (+ 1 (* -1 cosTheta)) cosTheta)>
#<alt -1>
#<alt (- (/ 1 cosTheta) 1)>
#<alt (- (/ 1 cosTheta) 1)>
#<alt (- (/ 1 cosTheta) 1)>
#<alt -1>
#<alt (- (/ 1 cosTheta) 1)>
#<alt (- (/ 1 cosTheta) 1)>
#<alt (- (/ 1 cosTheta) 1)>
#<alt (/ 1 cosTheta)>
#<alt (/ (+ 1 (* -3/2 (pow cosTheta 2))) cosTheta)>
#<alt (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 cosTheta) 3/2))) cosTheta)>
#<alt (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 cosTheta) 3/2))) cosTheta)>
#<alt (* 1/2 (pow cosTheta 2))>
#<alt (* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))>
#<alt (* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (* 3/2 (/ 1 cosTheta))))>
#<alt (* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (* 3/2 (/ 1 cosTheta))))>
#<alt (* 1/2 (pow cosTheta 2))>
#<alt (* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))>
#<alt (* (pow cosTheta 2) (+ 1/2 (* -1 (/ (- 3/2 (/ 1 (pow cosTheta 2))) cosTheta))))>
#<alt (* (pow cosTheta 2) (+ 1/2 (* -1 (/ (- 3/2 (/ 1 (pow cosTheta 2))) cosTheta))))>

Calls

75 calls:

Time	Variable		Point	Expression
59.0ms	cosTheta	@	-inf	(/ 1 (+ (* (exp (* cosTheta (neg cosTheta))) (/ (sqrt (/ (+ (* cosTheta -2) 1) (PI))) cosTheta)) 1))
3.0ms	cosTheta	@	inf	(/ 1 (+ (* (exp (* cosTheta (neg cosTheta))) (/ (sqrt (/ (+ (* cosTheta -2) 1) (PI))) cosTheta)) 1))
1.0ms	cosTheta	@	0	(/ 1 (+ (* (exp (* cosTheta (neg cosTheta))) (/ (sqrt (/ (+ (* cosTheta -2) 1) (PI))) cosTheta)) 1))
1.0ms	c	@	inf	(/ cosTheta (+ (* cosTheta (- c (sqrt (/ 1 (PI))))) (+ (/ 1 (sqrt (PI))) cosTheta)))
1.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (+ (* (sqrt (/ 1 (PI))) (+ (* cosTheta (+ (* cosTheta 1/2) -3/2)) (/ 1 cosTheta))) (neg (sqrt (/ 1 (PI)))))))

rewrite500.0ms (3.5%)

Memory

45.0MiB live, 509.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 358×	`lower-fma.f64`
3 344×	`lower-fma.f32`
3 236×	`lower-*.f64`
3 232×	`lower-*.f32`
3 160×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	241
0	78	237
1	356	215
2	3054	212
0	8210	210

Stop Event

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

Counts

26 → 925

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(*.f32 cosTheta (neg.f32 cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt.f32 (PI.f32))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal 1 binary32) (PI.f32))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(+.f32 #s(literal 1 binary32) c)
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(PI.f32)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))

Outputs
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))))
(exp.f32 (.f32 (log1p.f32 (.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))) #s(literal -1 binary32)))
(pow.f32 (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))) #s(literal -1 binary32))
(pow.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))) #s(literal -1/2 binary32))
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(/.f32 (neg.f32 (fma.f32 (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (neg.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) cosTheta))))
(/.f32 (neg.f32 (fma.f32 (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (/.f32 (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) cosTheta)))))
(/.f32 (neg.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (neg.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal -1 binary32) cosTheta))))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))))) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (neg.f32 (neg.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) cosTheta)))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))) (neg.f32 (neg.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)))))
(/.f32 (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))))) (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))))
(.f32 (fma.f32 (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) cosTheta))))
(.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal -1 binary32) cosTheta))))

simplify819.0ms (5.8%)

Memory

-9.6MiB live, 668.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 664×	`lower-fma.f64`
10 664×	`lower-fma.f32`
7 838×	`lower-*.f64`
7 838×	`lower-*.f32`
4 718×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	869	7500
1	2787	6904
0	8653	6594

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 294

Calls

Call 1

Inputs
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))))
(/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))))) (* (sqrt 2) (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ 1 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
1
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))
(+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(exp (* -1 (pow cosTheta 2)))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* -1 (pow cosTheta 2))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI)))))
(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI)))))
(/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) cosTheta)) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
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(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* -2 (/ cosTheta (PI)))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
-1
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
-1
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
(/ 1 cosTheta)
(/ (+ 1 (* -3/2 (pow cosTheta 2))) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 cosTheta) 3/2))) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 cosTheta) 3/2))) cosTheta)
(* 1/2 (pow cosTheta 2))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (* 3/2 (/ 1 cosTheta))))
(* 1/2 (pow cosTheta 2))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (- 3/2 (/ 1 (pow cosTheta 2))) cosTheta))))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (- 3/2 (/ 1 (pow cosTheta 2))) cosTheta))))

Outputs
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(*.f32 cosTheta (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (neg.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 cosTheta (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (neg.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32)))))) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32)))) (sqrt.f32 (PI.f32))))
(/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))
(+.f32 (/.f32 (fma.f32 #s(literal -1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (/.f32 (.f32 (.f32 #s(literal -1/4 binary32) cosTheta) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (.f32 cosTheta cosTheta))))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 #s(literal -2 binary32) (PI.f32))))) (neg.f32 (pow.f32 cosTheta #s(literal 4 binary32)))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))))
(-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (/.f32 (fma.f32 #s(literal -1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (/.f32 (.f32 (.f32 #s(literal -1/4 binary32) cosTheta) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (.f32 cosTheta cosTheta))))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 #s(literal -2 binary32) (PI.f32))))) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (.f32 #s(literal 1/16 binary32) (fma.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (.f32 cosTheta cosTheta))))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 4 binary32)) (PI.f32))))))) (pow.f32 cosTheta #s(literal 6 binary32)))) (fma.f32 #s(literal -1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (.f32 (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32)) (/.f32 (.f32 #s(literal -1/4 binary32) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (.f32 cosTheta cosTheta))))) (.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal -2 binary32))) (pow.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1 binary32)) #s(literal 3 binary32)))))))
(/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) #s(literal 1 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (pow.f32 (fma.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32))))) #s(literal 1 binary32))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
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(/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
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(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) cosTheta)) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta)
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(* cosTheta (sqrt (PI)))
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(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (sqrt (pow (PI) 3))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
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(/ 1 (- (+ 1 c) (sqrt (/ 1 (PI)))))
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(/ cosTheta (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c))) c)
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(/ (- (+ 1 (* -1 (/ (* (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (pow (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) 2)) (* (pow c 3) (pow cosTheta 2))))) (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (* (pow c 2) cosTheta))) (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))) c)
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))) 1) c))
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta c))) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (* (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (* c cosTheta)) (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (*.f32 cosTheta c)) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (* (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (pow (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) 2)) (* c (pow cosTheta 2))) (/ (* (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)) c)) (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) c)) 1) c))
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(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))))
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(* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI)))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (- (+ 1 (+ c (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))))
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(* cosTheta (- (+ 1 (+ c (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))))
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(* cosTheta (- (+ 1 (+ c (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))))
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(* -1 (* cosTheta (- (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- c (sqrt (/ 1 (PI)))))) 1)))
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(* c cosTheta)
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(* c (+ cosTheta (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ cosTheta c)))))
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(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) c)))))
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(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) c)))))
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(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) c)))))
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(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- c (sqrt (/ 1 (PI))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- c (sqrt (/ 1 (PI))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- c (sqrt (/ 1 (PI))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) (neg.f32 c) c)
(* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) (neg.f32 c) c)
(* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) (neg.f32 c) c)
c
(* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))
(neg.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) c (neg.f32 c)))
(* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))
(neg.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) c (neg.f32 c)))
(* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))
(neg.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) c (neg.f32 c)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
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(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))) (sqrt (/ 1 (PI)))))) cosTheta)
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (* -1 (/ (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))) c))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (/ (- (* -1 (/ (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (pow (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI)))) 2)) c)) (* -1 (* (- (sqrt (/ 1 (PI))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) (- (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta)))) (sqrt (/ 1 (PI))))))) c))) (+ 1 (* (sqrt (/ 1 (PI))) (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (/ 1 cosTheta))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (neg.f32 (.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32))) (-.f32 (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 (.f32 (neg.f32 cosTheta) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)))))) (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (neg.f32 (sqrt.f32 (PI.f32))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32))) (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) #s(literal 3/2 binary32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32)))) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32))))) (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (+.f32 (neg.f32 (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32))) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))) (*.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) (pow cosTheta 2)))))) (pow cosTheta 2))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
(/.f32 (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 2 binary32) (/.f32 (fma.f32 (.f32 #s(literal 4 binary32) (PI.f32)) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (fma.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -18 binary32) (.f32 (sqrt.f32 (PI.f32)) #s(literal -6 binary32)))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))) cosTheta)) (+ (* -4 (* (/ 1 cosTheta) (sqrt (PI)))) (* -3 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI))))))) cosTheta)))) (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (- (+ 1 c) (sqrt (/ 1 (PI)))))))) cosTheta)) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
(/.f32 (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 2 binary32) (/.f32 (+.f32 (/.f32 (fma.f32 (PI.f32) (.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) #s(literal -12 binary32)) (fma.f32 #s(literal -3 binary32) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32))) cosTheta) (-.f32 (.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -4 binary32)) (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32)))))) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -6 binary32))) (neg.f32 cosTheta))) (.f32 cosTheta cosTheta))
1
#s(literal 1 binary32)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
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c
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
c
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32)))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(.f32 cosTheta (fma.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (neg.f32 cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32)))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(neg.f32 (.f32 cosTheta (fma.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) #s(literal -1/8 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(neg.f32 (.f32 cosTheta (fma.f32 #s(literal 1/16 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))) (fma.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) #s(literal -1/8 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32))))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(fma.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(fma.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) #s(literal -1/2 binary32))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)) (fma.f32 #s(literal -1/16 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) #s(literal -1/2 binary32))))))
(/ 1 (PI))
(/.f32 #s(literal 1 binary32) (PI.f32))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(fma.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(fma.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(fma.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(* -2 (/ cosTheta (PI)))
(*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* -2 (/ cosTheta (PI)))
(*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)))))
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
-1
#s(literal -1 binary32)
(- (/ 1 cosTheta) 1)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(- (/ 1 cosTheta) 1)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(- (/ 1 cosTheta) 1)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
-1
#s(literal -1 binary32)
(- (/ 1 cosTheta) 1)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(- (/ 1 cosTheta) 1)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(- (/ 1 cosTheta) 1)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -3/2 (pow cosTheta 2))) cosTheta)
(/.f32 (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -3/2 binary32) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 cosTheta) 3/2))) cosTheta)
(/.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 cosTheta) 3/2))) cosTheta)
(/.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal 1 binary32)) cosTheta)
(* 1/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))))
(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))))
(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))))
(* 1/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (- 3/2 (/ 1 (pow cosTheta 2))) cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) cosTheta)))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (- 3/2 (/ 1 (pow cosTheta 2))) cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) cosTheta)))

eval246.0ms (1.7%)

Memory: 16.5MiB live, 445.0MiB allocated
Compiler: Compiled 51 200 to 6 482 computations (87.3% saved)

prune381.0ms (2.7%)

Memory

-0.1MiB live, 730.4MiB allocated

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	1 839	16	1 855
Fresh	15	13	28
Picked	4	1	5
Done	1	2	3
Total	1 859	32	1 891

Accuracy

100.0%

Counts

1 891 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.7%	(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.5%	(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
	95.7%	(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
	95.6%	(/.f32 cosTheta (*.f32 c (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 (/.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta c)))))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	97.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	96.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
	52.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)))
	95.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
	30.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta))) #s(literal 1 binary32)))
	52.9%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	52.8%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	47.8%	(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
	93.5%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	93.5%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
✓	93.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
✓	4.9%	(/.f32 #s(literal 1 binary32) c)
	93.6%	(.f32 (/.f32 cosTheta (fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (fma.f32 cosTheta cosTheta (.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	52.3%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
	32.0%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
	93.5%	(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
	94.1%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 2 628 to 833 computations (68.3% saved)

regimes192.0ms (1.3%)

Memory

-8.4MiB live, 351.4MiB allocated

Counts

86 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) c) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (*.f32 c (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 (/.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta c)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(/.f32 cosTheta (+.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (fma.f32 c (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c))))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1/2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (fma.f32 cosTheta cosTheta (.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (*.f32 cosTheta cosTheta))))))))
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))

Outputs

(*.f32 (/.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))

Calls

6 calls:

46.0ms	(+.f32 #s(literal 1 binary32) c)
44.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
26.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
24.0ms	c
23.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`c`
98.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.4%	1	`(+.f32 #s(literal 1 binary32) c)`
98.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes141.0ms (1%)

Memory

15.7MiB live, 406.1MiB allocated

Counts

85 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) c) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (*.f32 c (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 (/.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta c)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(/.f32 cosTheta (+.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (fma.f32 c (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c))))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1/2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (fma.f32 cosTheta cosTheta (.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (*.f32 cosTheta cosTheta))))))))

Outputs

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Calls

6 calls:

25.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
24.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
23.0ms	cosTheta
23.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
22.0ms	c

Results

Accuracy	Segments	Branch
97.9%	1	`c`
97.9%	1	`cosTheta`
97.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.9%	1	`(+.f32 #s(literal 1 binary32) c)`
97.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes140.0ms (1%)

Memory

-31.2MiB live, 365.6MiB allocated

Counts

82 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) c) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (*.f32 c (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 (/.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta c)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(/.f32 cosTheta (+.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (fma.f32 c (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c))))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1/2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (fma.f32 cosTheta cosTheta (.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Outputs

(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Calls

6 calls:

23.0ms	cosTheta
23.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
22.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
22.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
22.0ms	c

Results

Accuracy	Segments	Branch
97.9%	1	`cosTheta`
97.9%	1	`c`
97.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.9%	1	`(+.f32 #s(literal 1 binary32) c)`
97.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes139.0ms (1%)

Memory

0.3MiB live, 361.6MiB allocated

Counts

81 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) c) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (*.f32 c (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 (/.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta c)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(/.f32 cosTheta (+.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (fma.f32 c (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c))))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1/2 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (-.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (/.f32 c (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (fma.f32 cosTheta cosTheta (.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))
(pow.f32 (pow.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))

Calls

6 calls:

29.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
26.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
21.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
21.0ms	c
20.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.8%	1	`cosTheta`
97.8%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.8%	1	`(+.f32 #s(literal 1 binary32) c)`
97.8%	1	`c`
97.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes84.0ms (0.6%)

Memory

36.7MiB live, 193.6MiB allocated

Counts

49 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)))
(/.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)))) c) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 cosTheta (*.f32 c (+.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (neg.f32 (/.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta c)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))

Calls

6 calls:

15.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
15.0ms	c
14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
13.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
12.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.7%	1	`cosTheta`
97.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.7%	1	`c`
97.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.7%	1	`(+.f32 #s(literal 1 binary32) c)`
97.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes74.0ms (0.5%)

Memory

-32.7MiB live, 165.3MiB allocated

Counts

41 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))

Outputs

(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))

Calls

6 calls:

13.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
13.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
13.0ms	c
10.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.7%	1	`cosTheta`
97.7%	1	`c`
97.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.7%	1	`(+.f32 #s(literal 1 binary32) c)`
97.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes89.0ms (0.6%)

Memory

20.9MiB live, 103.4MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))

Calls

6 calls:

31.0ms	(+.f32 #s(literal 1 binary32) c)
22.0ms	c
9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
97.2%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.2%	1	`(+.f32 #s(literal 1 binary32) c)`
97.2%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.2%	1	`cosTheta`
97.2%	1	`c`
97.2%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes66.0ms (0.5%)

Memory

16.7MiB live, 92.9MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta c))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))

Outputs
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))

Calls

6 calls:

21.0ms	(+.f32 #s(literal 1 binary32) c)
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	c

Results

Accuracy	Segments	Branch
96.4%	1	`cosTheta`
96.4%	1	`c`
96.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.4%	1	`(+.f32 #s(literal 1 binary32) c)`
96.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes48.0ms (0.3%)

Memory

-50.4MiB live, 52.6MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))

Outputs
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))

Calls

6 calls:

15.0ms	(+.f32 #s(literal 1 binary32) c)
7.0ms	cosTheta
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
6.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
6.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
96.0%	1	`cosTheta`
96.0%	1	`c`
96.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.0%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes29.0ms (0.2%)

Memory

20.9MiB live, 55.9MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))

Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))

Calls

6 calls:

8.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	c
4.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.0%	1	`cosTheta`
96.0%	1	`c`
96.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.0%	1	`(+.f32 #s(literal 1 binary32) c)`
96.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes19.0ms (0.1%)

Memory

12.1MiB live, 51.6MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))

Outputs
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))

Calls

6 calls:

3.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
3.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	cosTheta
3.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
95.7%	1	`cosTheta`
95.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.7%	1	`c`
95.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.7%	1	`(+.f32 #s(literal 1 binary32) c)`
95.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes15.0ms (0.1%)

Memory

-9.0MiB live, 34.8MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))

Outputs
(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Calls

6 calls:

5.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
2.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
2.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	c
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
94.1%	1	`cosTheta`
94.1%	1	`c`
94.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
94.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
94.1%	1	`(+.f32 #s(literal 1 binary32) c)`
94.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes9.0ms (0.1%)

Memory

-13.2MiB live, 26.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)

Outputs
(/.f32 #s(literal 1 binary32) c)

Calls

6 calls:

2.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
1.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
1.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta
1.0ms	c

Results

Accuracy	Segments	Branch
4.9%	1	`cosTheta`
4.9%	1	`c`
4.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
4.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
4.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
4.9%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

simplify12.0ms (0.1%)

Memory

-12.1MiB live, 26.7MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary32`
32×	`+-commutative_binary32`
18×	`sub-neg_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	285
1	122	285
2	135	285
3	145	285
4	147	285

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) c)

Outputs
(.f32 (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)))) (fma.f32 cosTheta cosTheta (*.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (-.f32 (fma.f32 cosTheta (+.f32 (fma.f32 (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 cosTheta (sqrt.f32 (PI.f32))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) cosTheta) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) c)

soundness1.5s (10.9%)

Memory

54.8MiB live, 1 422.4MiB allocated

Rules

10 664×	`lower-fma.f64`
10 664×	`lower-fma.f32`
9 656×	`lower-fma.f64`
9 656×	`lower-fma.f32`
7 838×	`lower-*.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	440
0	90	437
1	409	422
2	3780	422
0	8151	422
0	39	241
0	78	237
1	356	215
2	3054	212
0	8210	210
0	48	314
0	94	314
1	407	273
2	3532	249
0	8201	247
0	869	7500
1	2787	6904
0	8653	6594
0	18	89
0	33	89
1	141	80
2	1060	73
0	8552	73
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311
0	1919	26114
1	6588	25560
0	8121	23969
0	1271	11675
1	4193	11304
0	8868	10791

Stop Event

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

Compiler

Compiled 558 to 277 computations (50.4% saved)

preprocess71.0ms (0.5%)

Memory: -16.2MiB live, 173.4MiB allocated
Compiler: Compiled 628 to 212 computations (66.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze30.0ms (0.2%)

sample2.1s (14.8%)

preprocess271.0ms (1.9%)

explain269.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify167.0ms (1.2%)

localize65.0ms (0.5%)

series24.0ms (0.2%)

rewrite300.0ms (2.1%)

simplify458.0ms (3.2%)

eval79.0ms (0.6%)

prune158.0ms (1.1%)

simplify356.0ms (2.5%)

localize226.0ms (1.6%)

series64.0ms (0.4%)

rewrite362.0ms (2.5%)

simplify470.0ms (3.3%)

eval135.0ms (1%)

prune175.0ms (1.2%)

simplify419.0ms (2.9%)

localize218.0ms (1.5%)

series163.0ms (1.1%)

rewrite402.0ms (2.8%)

simplify605.0ms (4.3%)

eval784.0ms (5.5%)

prune416.0ms (2.9%)

simplify488.0ms (3.4%)

localize259.0ms (1.8%)

series134.0ms (0.9%)

rewrite500.0ms (3.5%)

simplify819.0ms (5.8%)

eval246.0ms (1.7%)

prune381.0ms (2.7%)

regimes192.0ms (1.3%)

regimes141.0ms (1%)

regimes140.0ms (1%)

regimes139.0ms (1%)

regimes84.0ms (0.6%)

regimes74.0ms (0.5%)

regimes89.0ms (0.6%)

regimes66.0ms (0.5%)

regimes48.0ms (0.3%)

regimes29.0ms (0.2%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes9.0ms (0.1%)

simplify12.0ms (0.1%)

soundness1.5s (10.9%)

preprocess71.0ms (0.5%)

end0.0ms (0%)

Profiling