Metrics for Beckmann Sample, normalization factor

analyze37.0ms (0.3%)

Memory

-37.7MiB live, 50.3MiB 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)

sample2.3s (18.4%)

Memory

32.4MiB live, 2 774.1MiB allocated

Samples

1.8s	8 256×	0	valid
12.0ms	75×	0	invalid

Precisions

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

ival-div: 270.0ms (18.4% of total)

ival-sqrt: 213.0ms (14.5% of total)

ival-<: 178.0ms (12.2% of total)

ival-mult: 175.0ms (11.9% of total)

const: 151.0ms (10.3% of total)

ival-add: 147.0ms (10% of total)

ival-sub: 119.0ms (8.1% of total)

ival-exp: 80.0ms (5.5% of total)

ival-pi: 49.0ms (3.3% of total)

ival-neg: 44.0ms (3% of total)

ival-and: 22.0ms (1.5% of total)

exact: 15.0ms (1% of total)

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

Bogosity

preprocess234.0ms (1.9%)

Memory

-4.5MiB live, 187.4MiB 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)))

explain335.0ms (2.7%)

Memory

10.4MiB live, 455.1MiB 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

79.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 19.0ms (31.4% of total)

ival-div: 10.0ms (16.5% of total)

ival-pi: 8.0ms (13.2% of total)

ival-sqrt: 7.0ms (11.6% of total)

ival-add: 5.0ms (8.3% of total)

ival-sub: 5.0ms (8.3% of total)

ival-exp: 4.0ms (6.6% of total)

ival-neg: 2.0ms (3.3% 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

1.4MiB live, 1.4MiB 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)

simplify171.0ms (1.4%)

Memory

-4.2MiB live, 114.5MiB 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)

localize55.0ms (0.4%)

Memory

22.6MiB live, 97.9MiB 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

33.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-div: 5.0ms (22.8% of total)

ival-mult: 4.0ms (18.2% of total)

ival-sqrt: 4.0ms (18.2% of total)

ival-add: 3.0ms (13.7% of total)

ival-exp: 2.0ms (9.1% of total)

ival-sub: 2.0ms (9.1% of total)

ival-pi: 1.0ms (4.6% of total)

ival-neg: 1.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series30.0ms (0.2%)

Memory

-33.7MiB live, 48.8MiB 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
8.0ms	cosTheta	@	-inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
4.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
3.0ms	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))
1.0ms	cosTheta	@	-inf	(* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))

simplify420.0ms (3.4%)

Memory

12.8MiB live, 522.4MiB 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)))))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
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(/ (+ (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)
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(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
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(+ (* -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)))))))
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(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
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(/ (- (+ 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)
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(/ (- (+ 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)
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
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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 (sqrt (/ 1 (PI)))))))))))
(*.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))))
(* 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)))))))))))
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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)))
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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 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
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(/ (+ (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)
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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))

rewrite314.0ms (2.5%)

Memory

6.0MiB live, 540.3MiB 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)))
(/.f32 (neg.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (neg.f32 (*.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)
(/.f32 (neg.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 cosTheta))
(/.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (neg.f32 cosTheta) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)))
(.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(*.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32))))))
(*.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(*.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) #s(literal 1 binary32))
(*.f32 #s(literal -1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (neg.f32 cosTheta)))
(*.f32 (neg.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
(.f32 (neg.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) #s(literal 1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))))
(*.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
(*.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))
(*.f32 (neg.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 #s(literal -1 binary32) cosTheta))
(*.f32 (neg.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) #s(literal 1 binary32)))
(*.f32 (/.f32 #s(literal -1 binary32) cosTheta) (/.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))
(*.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (neg.f32 cosTheta)) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (neg.f32 cosTheta)) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(*.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) #s(literal 1/4 binary32)) cosTheta) (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) #s(literal 1/4 binary32)) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (sqrt.f32 (PI.f32)))) (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))
(*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))))
(*.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) #s(literal 1/4 binary32)) (sqrt.f32 (PI.f32))) (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) #s(literal 1/4 binary32)) cosTheta))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (sqrt.f32 (PI.f32)))) (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 (neg.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 (neg.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta))
(*.f32 (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (neg.f32 cosTheta)))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(neg.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (neg.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 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (sqrt.f32 (PI.f32))) (neg.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) (/.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))))
(/.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta)))
(/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 cosTheta (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))))
(/.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 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (/.f32 cosTheta (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))))
(/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) cosTheta)
(/.f32 (neg.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
(/.f32 (neg.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 (neg.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)))
(/.f32 (neg.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))))) (neg.f32 cosTheta))
(/.f32 (neg.f32 (neg.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 (neg.f32 (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (neg.f32 cosTheta))
(.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (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) (sqrt.f32 (PI.f32))) (/.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 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (sqrt.f32 (PI.f32))))
(.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (PI.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 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))
(.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) #s(literal 1 binary32)))
(.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta))
(.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) (sqrt.f32 (PI.f32))))
(.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))
(.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))
(.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta))
(.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)))
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(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (+.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta cosTheta cosTheta))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (neg.f32 (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta))) (.f32 cosTheta (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (*.f32 cosTheta (neg.f32 (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)))))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (+.f32 (neg.f32 cosTheta) #s(literal -1 binary32)) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))) (.f32 cosTheta (+.f32 (neg.f32 cosTheta) #s(literal -1 binary32))))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta))))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (*.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (+.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (neg.f32 (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta))) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (neg.f32 (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)))))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 (neg.f32 cosTheta) #s(literal -1 binary32)) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))) (*.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (+.f32 (neg.f32 cosTheta) #s(literal -1 binary32))))
(/.f32 (fma.f32 (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta)) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta cosTheta))))
(/.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 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (*.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (neg.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))))) (neg.f32 (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) #s(literal 1 binary32))
(/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 4 binary32) (.f32 cosTheta cosTheta)))) (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))
(/.f32 (neg.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))))) (neg.f32 (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 (neg.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)))) (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))))
(/.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))))

eval66.0ms (0.5%)

Memory: -9.8MiB live, 143.1MiB allocated
Compiler: Compiled 23 272 to 2 839 computations (87.8% saved)

prune131.0ms (1%)

Memory

23.5MiB live, 182.3MiB 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)))
	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)))))
	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)))))
▶	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)))))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))))
▶	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (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))))
	95.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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)))
	96.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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)))
▶	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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)))
	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	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)))
▶	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	96.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.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%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))

Compiler

Compiled 1 072 to 644 computations (39.9% saved)

simplify270.0ms (2.2%)

Memory

6.6MiB live, 444.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 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	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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)))
✓	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	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.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

11 282×	`lower-fma.f64`
11 276×	`lower-fma.f32`
3 204×	`lower-*.f64`
3 190×	`lower-*.f32`
2 062×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	669
0	112	669
1	199	648
2	435	624
3	994	624
4	2639	624
5	5212	624
0	8184	584

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

localize269.0ms (2.1%)

Memory

-17.8MiB live, 368.3MiB allocated

Localize:

Found 18 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	99.4%	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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)))
✓	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	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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	97.5%	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.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

106.0ms

256×

valid

Compiler

Compiled 591 to 55 computations (90.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-sqrt: 21.0ms (24.5% of total)

ival-div: 18.0ms (21% of total)

ival-mult: 18.0ms (21% of total)

ival-add: 11.0ms (12.8% of total)

ival-pow: 5.0ms (5.8% of total)

ival-exp: 4.0ms (4.7% of total)

ival-sub: 3.0ms (3.5% of total)

ival-cbrt: 2.0ms (2.3% of total)

ival-neg: 2.0ms (2.3% of total)

ival-pi: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series51.0ms (0.4%)

Memory

25.0MiB live, 100.9MiB allocated

Counts

22 → 384

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

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)>
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#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (* -1 (sqrt (/ 1 (PI))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<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 (/ (- c (sqrt (/ 1 (PI)))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) (/ 1 cosTheta)) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (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))))))>
#<alt (/ (+ cosTheta (+ (sqrt (/ 1 (PI))) (* cosTheta (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))))))) cosTheta)>
#<alt (+ 1 (+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))>
#<alt (+ 1 (+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))>
#<alt (+ 1 (+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (- (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI)))))))>
#<alt c>
#<alt (* 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))))))>
#<alt (* 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))))))>
#<alt (* 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))))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (- (+ 1 (+ (* (* cosTheta (- (* 1/2 cosTheta) 3/2)) (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) c)) 1)))>

Calls

96 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))))
3.0ms	cosTheta	@	inf	(/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))
3.0ms	cosTheta	@	-inf	(/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)
3.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))))
2.0ms	cosTheta	@	-inf	(/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))

simplify640.0ms (5.1%)

Memory

-0.9MiB live, 824.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 096×	`lower-fma.f64`
9 096×	`lower-fma.f32`
6 338×	`lower-+.f64`
6 338×	`lower-+.f32`
5 568×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	977	16977
1	3204	16340
0	8051	15605

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 372

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

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

rewrite308.0ms (2.5%)

Memory

-18.3MiB live, 494.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 530×	`lower-*.f64`
3 516×	`lower-*.f32`
3 334×	`lower-fma.f64`
3 328×	`lower-fma.f32`
2 938×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	480
0	112	480
1	458	415
2	3898	391
0	8352	391

Stop Event

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

Counts

22 → 523

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

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

eval125.0ms (1%)

Memory: 33.0MiB live, 296.6MiB allocated
Compiler: Compiled 40 455 to 3 984 computations (90.2% saved)

prune227.0ms (1.8%)

Memory

-13.4MiB live, 350.0MiB allocated

Pruning

38 alts after pruning (37 fresh and 1 done)

	Pruned	Kept	Total
New	1 041	31	1 072
Fresh	11	6	17
Picked	4	1	5
Done	0	0	0
Total	1 056	38	1 094

Accuracy

99.9%

Counts

1 094 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.4%	(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	52.5%	(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) #s(literal -1/2 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))))))))
	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)))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) c))
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (exp.f32 (*.f32 cosTheta cosTheta)) 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)) #s(approx (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta) (/.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) #s(approx (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))))
	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32))))))))
	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
▶	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
	52.3%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (-.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (pow (cbrt (PI)) -3/2) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (pow (cbrt (PI)) -3/2) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (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))))
	96.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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)))
	95.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (-.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta #s(approx (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) (.f32 c (fma.f32 cosTheta (/.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)) #s(literal -1 binary32))) c) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) cosTheta))))) cosTheta)))
	92.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta #s(approx (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))
	97.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.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)))) cosTheta)))))
	51.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (+.f32 c (.f32 c (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 (*.f32 cosTheta (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)))))))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (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))))))
▶	33.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (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))))))
	28.0%	(.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 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))))
	52.3%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (-.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	87.9%	(exp.f32 (.f32 (log1p.f32 (+.f32 c #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) #s(literal -1 binary32)))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.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%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
	96.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (pow (cbrt (PI)) -3/2) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.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)))))
✓	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 2 026 to 1 088 computations (46.3% saved)

simplify320.0ms (2.6%)

Memory

-19.5MiB live, 535.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(/.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))
✓	cost-diff	64	(/.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))
✓	cost-diff	352	(.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))))
✓	cost-diff	576	(-.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)))
✓	cost-diff	0	(+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	cost-diff	0	(/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
✓	cost-diff	0	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))
✓	cost-diff	0	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
✓	cost-diff	0	#s(approx (+ 1 c) #s(literal 1 binary32))
✓	cost-diff	0	(+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) 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	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (exp.f32 (*.f32 cosTheta cosTheta)) cosTheta)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (exp.f32 (*.f32 cosTheta cosTheta)) cosTheta))))
✓	cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))

Rules

9 656×	`lower-fma.f64`
9 646×	`lower-fma.f32`
2 832×	`lower-*.f64`
2 818×	`lower-*.f32`
2 028×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	1066
0	139	1066
1	272	989
2	637	985
3	1574	968
4	5210	960
0	8234	919

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

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

localize276.0ms (2.2%)

Memory

29.5MiB live, 552.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.0%	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
✓	accuracy	97.1%	(+.f32 (neg.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -1 binary32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	40.4%	(.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))))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))
✓	accuracy	98.3%	(/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	94.8%	#s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (*.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))))
✓	accuracy	98.3%	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
✓	accuracy	97.5%	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.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	95.3%	#s(approx (+ 1 c) #s(literal 1 binary32))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	94.3%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	99.7%	(*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (exp.f32 (*.f32 cosTheta cosTheta)) cosTheta))))
✓	accuracy	98.3%	(/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (exp.f32 (*.f32 cosTheta cosTheta)) cosTheta))
✓	accuracy	97.4%	(sqrt.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))

Samples

140.0ms

256×

valid

Compiler

Compiled 730 to 72 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 115.0ms

ival-mult: 45.0ms (39% of total)

ival-div: 24.0ms (20.8% of total)

ival-add: 16.0ms (13.9% of total)

ival-sub: 10.0ms (8.7% of total)

ival-sqrt: 10.0ms (8.7% of total)

ival-exp: 6.0ms (5.2% of total)

ival-neg: 3.0ms (2.6% of total)

ival-pi: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series98.0ms (0.8%)

Memory

-28.9MiB live, 88.5MiB allocated

Counts

27 → 456

Calls

Call 1

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

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

Calls

114 calls:

Time	Variable		Point	Expression
35.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta))))
26.0ms	c	@	inf	(* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) 1/2) (/ (+ (* (sqrt (/ 1 (PI))) 3/2) (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta))) (neg cosTheta))))
4.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta))))
1.0ms	c	@	0	(* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) 1/2) (/ (+ (* (sqrt (/ 1 (PI))) 3/2) (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta))) (neg cosTheta))))
1.0ms	c	@	-inf	(* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) 1/2) (/ (+ (* (sqrt (/ 1 (PI))) 3/2) (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta))) (neg cosTheta))))

simplify393.0ms (3.1%)

Memory

21.5MiB live, 810.4MiB allocated

Algorithm

1×	egg-herbie

Rules

6 524×	`lower-*.f64`
6 524×	`lower-*.f32`
5 790×	`lower-fma.f64`
5 790×	`lower-fma.f32`
4 632×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1126	16366
1	3719	15413
0	8077	14908

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 438

Calls

Call 1

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

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

rewrite382.0ms (3.1%)

Memory

-11.3MiB live, 669.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 558×	`lower-*.f64`
4 544×	`lower-*.f32`
4 220×	`lower-fma.f64`
4 210×	`lower-fma.f32`
2 142×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	84	602
0	130	604
1	575	440
2	5734	440
0	8713	440

Stop Event

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

Counts

27 → 657

Calls

Call 1

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

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

eval342.0ms (2.7%)

Memory: 39.1MiB live, 428.6MiB allocated
Compiler: Compiled 63 728 to 7 354 computations (88.5% saved)

prune275.0ms (2.2%)

Memory

-25.1MiB live, 585.6MiB allocated

Pruning

44 alts after pruning (41 fresh and 3 done)

	Pruned	Kept	Total
New	1 624	29	1 653
Fresh	20	12	32
Picked	3	2	5
Done	0	1	1
Total	1 647	44	1 691

Accuracy

100.0%

Counts

1 691 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.5%	(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) #s(literal -1/2 binary32))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) c))
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32)))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) 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)) #s(approx (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta) (/.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) #s(approx (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))))
✓	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (/.f32 (*.f32 cosTheta (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))))
	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))))
▶	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32))))))))
	52.3%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) (/.f32 #s(literal 1 binary32) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))))
	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta))) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (pow (cbrt (PI)) -3/2) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (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))))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)))
	97.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 (-.f32 (.f32 (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)) (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (-.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta #s(approx (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) (.f32 c (fma.f32 cosTheta (/.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)) #s(literal -1 binary32))) c) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) cosTheta))))) cosTheta)))
▶	97.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)))))
	47.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) cosTheta))) (/.f32 #s(literal -1 binary32) cosTheta) (.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32))))))))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (+.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)) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))))
	51.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (+.f32 c (.f32 c (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 (*.f32 cosTheta (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)))))))
	33.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) cosTheta)) cosTheta)) (*.f32 cosTheta cosTheta)))))
	33.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.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 #s(approx (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))) (neg.f32 cosTheta))) (neg.f32 cosTheta)))))))
▶	33.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.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 #s(literal -1 binary32) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) (neg.f32 cosTheta)))))))
	29.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.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) #s(approx (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (neg.f32 cosTheta))))) (neg.f32 cosTheta)))))))
	33.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 cosTheta) (-.f32 (/.f32 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) cosTheta)))))))))
	29.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) #s(approx (/ (+ (* (sqrt (/ 1 (PI))) 3/2) (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta))) (neg cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 cosTheta cosTheta)))))))))
	52.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (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))))))
	28.0%	(.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 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))))
	52.3%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	96.4%	#s(approx (/ 1 (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta)))) (*.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) (sqrt.f32 (PI.f32)))))
▶	93.7%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.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%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 3/2 binary32))))
✓	94.1%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 2 341 to 1 256 computations (46.3% saved)

simplify309.0ms (2.5%)

Memory

6.2MiB live, 429.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32) (.f32 (/.f32 #s(literal -1 binary32) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) (neg.f32 cosTheta))
✓	cost-diff	160	(.f32 (/.f32 #s(literal -1 binary32) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
✓	cost-diff	352	(.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 #s(literal -1 binary32) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) (neg.f32 cosTheta))))
✓	cost-diff	672	(-.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) cosTheta)
✓	cost-diff	0	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)))))
✓	cost-diff	448	(.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)))
✓	cost-diff	0	#s(approx (+ 1 c) #s(literal 1 binary32))
✓	cost-diff	0	(+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
✓	cost-diff	352	(*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (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	0	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (/.f32 #s(literal 1 binary32) (/.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 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32)))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32)))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta))))
✓	cost-diff	576	(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32))))

Rules

9 378×	`lower-fma.f64`
9 368×	`lower-fma.f32`
3 570×	`lower-*.f64`
3 552×	`lower-*.f32`
1 866×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	1157
0	157	1147
1	310	1092
2	716	1035
3	1728	995
4	5757	991
0	8259	950

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

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

localize318.0ms (2.5%)

Memory

8.5MiB live, 610.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	97.1%	(-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	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	40.4%	(.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 #s(literal -1 binary32) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) (neg.f32 cosTheta))))
✓	accuracy	98.0%	(fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)
✓	accuracy	97.2%	(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	94.8%	#s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
✓	accuracy	98.1%	(*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
✓	accuracy	97.5%	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	95.3%	#s(approx (+ 1 c) #s(literal 1 binary32))
✓	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	94.3%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
✓	accuracy	98.9%	(*.f32 (PI.f32) cosTheta)
✓	accuracy	98.4%	(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32))))
✓	accuracy	98.3%	(/.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32)))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta))
✓	accuracy	97.4%	(sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32))))))

Samples

143.0ms

256×

valid

Compiler

Compiled 765 to 85 computations (88.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-div: 34.0ms (30.2% of total)

ival-mult: 31.0ms (27.5% of total)

ival-add: 19.0ms (16.9% of total)

ival-sqrt: 12.0ms (10.7% of total)

ival-exp: 6.0ms (5.3% of total)

ival-sub: 6.0ms (5.3% of total)

ival-neg: 2.0ms (1.8% of total)

ival-pi: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

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

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

series52.0ms (0.4%)

Memory

17.1MiB live, 55.3MiB allocated

Counts

31 → 504

Calls

Call 1

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

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

Calls

126 calls:

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

simplify434.0ms (3.5%)

Memory

16.2MiB live, 690.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 528×	`lower-*.f64`
6 528×	`lower-*.f32`
6 086×	`lower-fma.f64`
6 086×	`lower-fma.f32`
4 760×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1141	16595
1	3736	15602
0	8070	15025

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 486

Calls

Call 1

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

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

rewrite449.0ms (3.6%)

Memory

6.1MiB live, 630.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 982×	`lower-*.f64`
3 964×	`lower-*.f32`
3 086×	`lower-fma.f64`
3 076×	`lower-fma.f32`
2 710×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	674
0	148	658
1	674	537
2	6681	537
0	8493	527

Stop Event

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

Counts

31 → 588

Calls

Call 1

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

Outputs
(+.f32 (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))))
(+.f32 (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 cosTheta (.f32 cosTheta (PI.f32))))
(fma.f32 cosTheta (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))))
(fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (*.f32 cosTheta (PI.f32))))
(fma.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))))
(fma.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) cosTheta (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))))
(fma.f32 #s(literal -2 binary32) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) cosTheta) (/.f32 cosTheta (.f32 cosTheta (PI.f32))))
(fma.f32 (/.f32 #s(literal -2 binary32) (PI.f32)) cosTheta (/.f32 cosTheta (*.f32 cosTheta (PI.f32))))
(fma.f32 (.f32 cosTheta #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (+.f32 (pow.f32 (/.f32 cosTheta (.f32 cosTheta (PI.f32))) #s(literal 3 binary32)) (pow.f32 (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (-.f32 (.f32 (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32)))) (.f32 (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32)))))))
(/.f32 (-.f32 (.f32 (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))) (.f32 (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32))))) (-.f32 (/.f32 cosTheta (.f32 cosTheta (PI.f32))) (/.f32 cosTheta (.f32 (PI.f32) #s(literal -1/2 binary32)))))
(/.f32 (.f32 cosTheta (fma.f32 cosTheta (.f32 (PI.f32) #s(literal -2 binary32)) (PI.f32))) (.f32 (PI.f32) (.f32 cosTheta (PI.f32))))
(/.f32 (.f32 cosTheta (fma.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 cosTheta (PI.f32)))) (/.f32 #s(literal -8 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 cosTheta (PI.f32)))) (-.f32 (/.f32 #s(literal 4 binary32) (.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal -2 binary32) (.f32 (PI.f32) (*.f32 cosTheta (PI.f32)))))))
(/.f32 (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 cosTheta (PI.f32)))) (/.f32 #s(literal 4 binary32) (.f32 (PI.f32) (PI.f32))))) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(/.f32 (.f32 (fma.f32 cosTheta (.f32 (PI.f32) #s(literal -2 binary32)) (PI.f32)) cosTheta) (.f32 (PI.f32) (.f32 cosTheta (PI.f32))))
(/.f32 (.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 cosTheta (PI.f32)))) (/.f32 #s(literal -8 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 cosTheta (PI.f32)))) (-.f32 (/.f32 #s(literal 4 binary32) (.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal -2 binary32) (.f32 (PI.f32) (*.f32 cosTheta (PI.f32)))))))
(/.f32 (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 cosTheta (PI.f32)))) (/.f32 #s(literal 4 binary32) (.f32 (PI.f32) (PI.f32)))) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))) cosTheta)
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 #s(approx ( (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c)) #s(literal -1 binary32)))
(pow.f32 (fma.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal -1 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (fma.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx ( (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx ( (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal 1 binary32))
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(.f32 (fma.f32 (.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))) (.f32 cosTheta (.f32 #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (-.f32 cosTheta (.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))) (.f32 cosTheta (.f32 #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))))))))
(.f32 (.f32 (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta))))
(.f32 (+.f32 #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) cosTheta)
(neg.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32))) #s(literal -1 binary32)))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal -1/2 binary32)))
(exp.f32 (*.f32 (neg.f32 (log.f32 (PI.f32))) #s(literal 1/2 binary32)))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.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 #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 (pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/4 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/4 binary32)))
(neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(exp.f32 (*.f32 (log.f32 (neg.f32 (sqrt.f32 (PI.f32)))) #s(literal -1 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))) #s(literal -1 binary32)))
(pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32))
(pow.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) #s(literal 1 binary32)) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (*.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (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 #s(literal -1 binary32) (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
(+.f32 (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal -1 binary32))
(+.f32 (-.f32 #s(literal -1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(pow.f32 (/.f32 (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (-.f32 #s(literal 1 binary32) (*.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) #s(literal -1 binary32))
(fma.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal -1 binary32))
(fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal -1 binary32) #s(literal -1 binary32))
(-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
(-.f32 (-.f32 #s(literal -1 binary32) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(-.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))) (/.f32 (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))))
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (/.f32 (*.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(-.f32 (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) c)
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (-.f32 #s(literal 1 binary32) (*.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))))
(/.f32 (-.f32 #s(literal -1 binary32) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
(/.f32 (neg.f32 (-.f32 #s(literal -1 binary32) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) (neg.f32 (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (.f32 #s(literal -1 binary32) (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal -1 binary32) c) #s(literal 3 binary32)) (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (-.f32 #s(literal -1 binary32) c) (-.f32 #s(literal -1 binary32) c) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal -1 binary32) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (-.f32 #s(literal -1 binary32) (neg.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 (-.f32 (*.f32 (-.f32 #s(literal -1 binary32) c) (-.f32 #s(literal -1 binary32) c)) (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (-.f32 #s(literal -1 binary32) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
(.f32 (-.f32 #s(literal -1 binary32) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (*.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))

eval154.0ms (1.2%)

Memory: -11.9MiB live, 395.2MiB allocated
Compiler: Compiled 48 125 to 4 382 computations (90.9% saved)

prune235.0ms (1.9%)

Memory

2.8MiB live, 491.9MiB allocated

Pruning

45 alts after pruning (41 fresh and 4 done)

	Pruned	Kept	Total
New	1 160	16	1 176
Fresh	11	25	36
Picked	3	2	5
Done	1	2	3
Total	1 175	45	1 220

Accuracy

100.0%

Counts

1 220 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.5%	(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) #s(literal -1/2 binary32))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 #s(approx ( (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 cosTheta (*.f32 cosTheta (PI.f32)))))) (+.f32 #s(literal 1 binary32) c)))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) c))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (/.f32 (.f32 (fma.f32 cosTheta (.f32 (PI.f32) #s(literal -2 binary32)) (PI.f32)) cosTheta) (.f32 (PI.f32) (.f32 cosTheta (PI.f32)))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta))))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (sqrt.f32 #s(approx (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta)) (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta)) (/.f32 #s(literal -2 binary32) (PI.f32)))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (*.f32 (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))))))
	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))))
✓	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32))))))))
	52.3%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) (/.f32 #s(literal 1 binary32) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))))
	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (- (- 1 cosTheta) cosTheta))) (* (exp (* cosTheta cosTheta)) cosTheta))) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (pow (cbrt (PI)) -3/2) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	97.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) cosTheta))))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (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))))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)))
	97.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 (-.f32 (.f32 (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)) (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (-.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (+.f32 cosTheta #s(approx (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI)))) (.f32 c (fma.f32 cosTheta (/.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)) #s(literal -1 binary32))) c) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) cosTheta))))) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta))) #s(literal 1 binary32)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (fma.f32 cosTheta #s(approx (+ ( cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))))
	97.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 (/.f32 (fma.f32 cosTheta #s(approx (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI))))) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	97.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (+.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)) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))))
	51.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (+.f32 c (.f32 c (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 (*.f32 cosTheta (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)))))))
	33.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) cosTheta)) cosTheta)) (*.f32 cosTheta cosTheta)))))
	33.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.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 #s(literal -1 binary32) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) #s(approx (- -1 (+ c (/ -1 (sqrt (PI))))) (neg.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))) (neg.f32 cosTheta)))))))
	29.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.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) #s(approx (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (neg.f32 cosTheta))))) (neg.f32 cosTheta)))))))
	33.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 cosTheta) (-.f32 (/.f32 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 #s(literal -1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) cosTheta)))))))))
	29.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) #s(approx (/ (+ (* (sqrt (/ 1 (PI))) 3/2) (/ (- (/ (sqrt (/ 1 (PI))) cosTheta) (+ (neg (- c (sqrt (/ 1 (PI))))) -1)) (neg cosTheta))) (neg cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 cosTheta cosTheta)))))))))
	33.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ cosTheta (+ (* cosTheta (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* cosTheta 1/2) -3/2))) (- c (sqrt (/ 1 (PI)))))) (sqrt (/ 1 (PI))))) cosTheta) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32) #s(approx (/ (+ (* (sqrt (/ 1 (PI))) 3/2) (* (/ -1 cosTheta) (- (/ 1 (* cosTheta (sqrt (PI)))) (- -1 (+ c (/ -1 (sqrt (PI)))))))) (neg 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)) (.f32 cosTheta (.f32 cosTheta cosTheta)))))))))
	28.0%	(.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 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))))
	52.3%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))) (-.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta)))))
✓	93.7%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.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%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 3/2 binary32))))
✓	94.1%	#s(approx (/ 1 (+ (+ 1 c) (/ 1 (/ (sqrt (PI)) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 3 651 to 1 112 computations (69.5% saved)

regimes175.0ms (1.4%)

Memory

-0.3MiB live, 388.9MiB allocated

Counts

99 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

31.0ms	(+.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))))
30.0ms	(/.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)))))
28.0ms	cosTheta
27.0ms	(.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)))
27.0ms	c

Results

Accuracy	Segments	Branch
98.0%	1	`cosTheta`
98.0%	1	`c`
98.0%	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)))))`
98.0%	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))))`
98.0%	1	`(+.f32 #s(literal 1 binary32) c)`
98.0%	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)

regimes157.0ms (1.3%)

Memory

-17.6MiB live, 347.7MiB allocated

Counts

86 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

30.0ms	(.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)))
27.0ms	c
27.0ms	(/.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 #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))))
23.0ms	cosTheta

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)

regimes148.0ms (1.2%)

Memory

19.6MiB live, 171.4MiB allocated

Counts

48 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

58.0ms	(+.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))))
31.0ms	(.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)))
17.0ms	cosTheta
15.0ms	c
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)))))

Results

Accuracy	Segments	Branch
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)))))`
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)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes357.0ms (2.9%)

Memory

-146.0MiB live, 187.2MiB allocated

Counts

44 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

279.0ms	(.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)))
18.0ms	c
17.0ms	(/.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)))))
16.0ms	cosTheta
12.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.2%	1	`cosTheta`
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)))))`
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	`c`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes74.0ms (0.6%)

Memory

24.1MiB live, 185.0MiB allocated

Counts

41 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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)))))
12.0ms	c
12.0ms	(+.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))))
11.0ms	(.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)))
11.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.7%	1	`cosTheta`
96.7%	1	`c`
96.7%	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)))))`
96.7%	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))))`
96.7%	1	`(+.f32 #s(literal 1 binary32) c)`
96.7%	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)

regimes72.0ms (0.6%)

Memory

-23.8MiB live, 173.5MiB allocated

Counts

40 → 1

Calls

Call 1

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

Outputs

#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.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:

13.0ms	c
12.0ms	(.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	(/.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)))))
12.0ms	cosTheta
11.0ms	(+.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))))

Results

Accuracy	Segments	Branch
96.4%	1	`cosTheta`
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	`c`
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 (.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)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes40.0ms (0.3%)

Memory

20.3MiB live, 99.6MiB allocated

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

8.0ms	c
7.0ms	(.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)))))
6.0ms	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 (.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)

regimes34.0ms (0.3%)

Memory

3.5MiB live, 81.9MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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)))))
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)))
5.0ms	(+.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))))
5.0ms	c
5.0ms	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)

regimes28.0ms (0.2%)

Memory

-27.9MiB live, 62.6MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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)))))
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	(.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	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
96.0%	1	`cosTheta`
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	`c`
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)

regimes20.0ms (0.2%)

Memory

10.9MiB live, 50.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

4.0ms	c
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 #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	(+.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

Results

Accuracy	Segments	Branch
94.1%	1	`cosTheta`
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	`c`
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

-15.2MiB live, 24.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	cosTheta
1.0ms	(.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	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

23.8MiB live, 23.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	608
1	127	608
2	140	608
3	147	608
4	150	608

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (9.6%)

Memory

0.9MiB live, 721.1MiB allocated

Rules

9 656×	`lower-fma.f64`
9 656×	`lower-fma.f32`
9 096×	`lower-fma.f64`
9 096×	`lower-fma.f32`
6 338×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	480
0	112	480
1	458	415
2	3898	391
0	8352	391
0	84	602
0	130	604
1	575	440
2	5734	440
0	8713	440
0	94	674
0	148	658
1	674	537
2	6681	537
0	8493	527
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311
0	977	16977
1	3204	16340
0	8051	15605

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

Compiler

Compiled 564 to 271 computations (52% saved)

preprocess177.0ms (1.4%)

Memory: -20.7MiB live, 135.4MiB allocated
Compiler: Compiled 518 to 150 computations (71% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze37.0ms (0.3%)

sample2.3s (18.4%)

preprocess234.0ms (1.9%)

explain335.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify171.0ms (1.4%)

localize55.0ms (0.4%)

series30.0ms (0.2%)

simplify420.0ms (3.4%)

rewrite314.0ms (2.5%)

eval66.0ms (0.5%)

prune131.0ms (1%)

simplify270.0ms (2.2%)

localize269.0ms (2.1%)

series51.0ms (0.4%)

simplify640.0ms (5.1%)

rewrite308.0ms (2.5%)

eval125.0ms (1%)

prune227.0ms (1.8%)

simplify320.0ms (2.6%)

localize276.0ms (2.2%)

series98.0ms (0.8%)

simplify393.0ms (3.1%)

rewrite382.0ms (3.1%)

eval342.0ms (2.7%)

prune275.0ms (2.2%)

simplify309.0ms (2.5%)

localize318.0ms (2.5%)

series52.0ms (0.4%)

simplify434.0ms (3.5%)

rewrite449.0ms (3.6%)

eval154.0ms (1.2%)

prune235.0ms (1.9%)

regimes175.0ms (1.4%)

regimes157.0ms (1.3%)

regimes148.0ms (1.2%)

regimes357.0ms (2.9%)

regimes74.0ms (0.6%)

regimes72.0ms (0.6%)

regimes40.0ms (0.3%)

regimes34.0ms (0.3%)

regimes28.0ms (0.2%)

regimes20.0ms (0.2%)

regimes9.0ms (0.1%)

simplify12.0ms (0.1%)

soundness1.2s (9.6%)

preprocess177.0ms (1.4%)

end0.0ms (0%)

Profiling