Metrics for Beckmann Sample, normalization factor

analyze143.0ms (1.1%)

Memory

-12.4MiB live, 64.8MiB 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)

sample1.9s (14.1%)

Memory

104.5MiB live, 3 026.4MiB allocated

Samples

1.4s	8 256×	0	valid
8.0ms	61×	0	invalid

Precisions

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

ival-div: 201.0ms (16.8% of total)

ival-mult: 169.0ms (14.1% of total)

ival-sub: 162.0ms (13.5% of total)

const: 141.0ms (11.8% of total)

ival-sqrt: 125.0ms (10.4% of total)

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

ival-pi: 86.0ms (7.2% of total)

ival-<: 77.0ms (6.4% of total)

ival-exp: 67.0ms (5.6% of total)

ival-neg: 33.0ms (2.8% of total)

ival-and: 23.0ms (1.9% of total)

exact: 14.0ms (1.2% of total)

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

Bogosity

preprocess227.0ms (1.7%)

Memory

-29.1MiB live, 192.3MiB 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)))

explain257.0ms (1.9%)

Memory

-1.1MiB live, 386.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
1	-	-	`(-.f32 (-.f32 #s(literal 1 binary32) 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) (+.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	-	-	`(-.f32 #s(literal 1 binary32) 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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	0	0
-	1	255

Precision

0.0

Recall

0/0

Confusion?

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

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

0.0

Recall?

0/0

Samples

93.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-div: 11.0ms (22.1% of total)

ival-mult: 11.0ms (22.1% of total)

ival-sqrt: 7.0ms (14.1% of total)

ival-add: 6.0ms (12.1% of total)

ival-exp: 5.0ms (10% of total)

ival-sub: 5.0ms (10% of total)

ival-pi: 2.0ms (4% of total)

ival-neg: 2.0ms (4% 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
▶	97.7%	(/.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

▶

97.7%

(/.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)

simplify189.0ms (1.4%)

Memory

-34.7MiB live, 118.4MiB 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)

localize98.0ms (0.7%)

Memory

15.0MiB live, 90.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.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)))))
✓	accuracy	98.0%	(*.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

30.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-div: 5.0ms (23.4% of total)

ival-mult: 4.0ms (18.7% of total)

ival-add: 3.0ms (14% of total)

ival-sqrt: 3.0ms (14% of total)

ival-exp: 2.0ms (9.4% of total)

ival-sub: 2.0ms (9.4% of total)

ival-pi: 1.0ms (4.7% of total)

ival-neg: 1.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

3.9MiB live, 42.0MiB 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)>
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#<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)))))))))))>
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#<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
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)))))
3.0ms	c	@	0	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
2.0ms	cosTheta	@	inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
2.0ms	cosTheta	@	-inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))

simplify432.0ms (3.3%)

Memory

18.7MiB live, 607.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 82

Calls

Call 1

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

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

rewrite366.0ms (2.8%)

Memory

-23.6MiB live, 533.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

6 → 473

Calls

Call 1

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

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

eval92.0ms (0.7%)

Memory: 7.2MiB live, 158.7MiB allocated
Compiler: Compiled 23 272 to 2 839 computations (87.8% saved)

prune151.0ms (1.1%)

Memory

7.0MiB live, 278.4MiB allocated

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	531	24	555
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	531	25	556

Accuracy

99.8%

Counts

556 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	90.4%	(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))
▶	90.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	90.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) cosTheta) (*.f32 cosTheta (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	91.1%	(/.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)))))
	91.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.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))))
	91.1%	(/.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)))))
✓	97.7%	(/.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)))))
	96.8%	(/.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 (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))))
	96.2%	(/.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 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))))
	94.5%	(/.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))))
	91.2%	(/.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
▶	97.9%	(/.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))))
	97.4%	(/.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))))
	54.9%	(/.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))))
▶	94.4%	(/.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)))
	96.1%	(/.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)))
	96.8%	(/.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)))
	91.4%	(/.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)))
	54.9%	(/.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 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))))
	97.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 c (fma.f32 c (-.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (/.f32 c (pow.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) #s(literal 4 binary32)))) (/.f32 #s(literal -1 binary32) (pow.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))))
▶	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	95.1%	#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)))))
	97.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (-.f32 (.f32 (.f32 (PI.f32) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.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)))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (neg.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))) (neg.f32 cosTheta) (fma.f32 (PI.f32) (.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)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.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)))))
	92.1%	#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 1 459 to 778 computations (46.7% saved)

simplify302.0ms (2.3%)

Memory

-1.1MiB live, 438.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f32 c c #s(literal -1 binary32))
✓	cost-diff	160	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))))
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
✓	cost-diff	512	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta))
✓	cost-diff	0	(/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta)
✓	cost-diff	0	(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))
✓	cost-diff	0	#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)))
✓	cost-diff	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 (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))))
✓	cost-diff	0	(/.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)
✓	cost-diff	0	#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))
✓	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 (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)))
✓	cost-diff	576	(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))))
✓	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

9 582×	`lower-fma.f64`
9 572×	`lower-fma.f32`
2 588×	`lower-*.f64`
2 572×	`lower-*.f32`
1 742×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	612
0	119	613
1	196	582
2	380	575
3	816	575
4	1820	559
5	4475	559
0	8273	538

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

localize227.0ms (1.7%)

Memory

-1.1MiB live, 541.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
✓	accuracy	98.4%	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta))
✓	accuracy	97.6%	(sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))
✓	accuracy	99.6%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.1%	(/.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))))
✓	accuracy	98.1%	(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))
✓	accuracy	97.6%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	98.2%	(/.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)
✓	accuracy	96.9%	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	96.5%	#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))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	5.0%	#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	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.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	98.0%	(*.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

115.0ms

256×

valid

Compiler

Compiled 552 to 62 computations (88.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-div: 25.0ms (27.2% of total)

ival-mult: 22.0ms (23.9% of total)

ival-add: 17.0ms (18.5% of total)

ival-sqrt: 8.0ms (8.7% of total)

ival-exp: 6.0ms (6.5% of total)

ival-pow: 5.0ms (5.4% of total)

ival-sub: 4.0ms (4.4% of total)

ival-cbrt: 2.0ms (2.2% of total)

ival-neg: 2.0ms (2.2% of total)

ival-pi: 1.0ms (1.1% of total)

exact: 1.0ms (1.1% of total)

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

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

series199.0ms (1.5%)

Memory

13.4MiB live, 130.8MiB allocated

Counts

26 → 468

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

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

Calls

117 calls:

Time	Variable		Point	Expression
129.0ms	c	@	inf	(/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta)
6.0ms	cosTheta	@	inf	(sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI)))
5.0ms	cosTheta	@	0	(/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta)))
4.0ms	cosTheta	@	-inf	(/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta)))
4.0ms	cosTheta	@	-inf	(+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta))))))

simplify384.0ms (2.9%)

Memory

-14.0MiB live, 615.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 838×	`lower-*.f64`
6 838×	`lower-*.f32`
6 366×	`lower-fma.f64`
6 366×	`lower-fma.f32`
4 620×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1094	20423
1	3658	19698
0	8099	18799

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 452

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

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

rewrite382.0ms (2.9%)

Memory

35.6MiB live, 548.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 072×	`lower-fma.f64`
4 062×	`lower-fma.f32`
3 418×	`lower-*.f64`
3 402×	`lower-*.f32`
2 658×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	484
0	119	485
1	460	418
2	3823	398
0	8301	398

Stop Event

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

Counts

26 → 843

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

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

eval252.0ms (1.9%)

Memory: -8.2MiB live, 295.9MiB allocated
Compiler: Compiled 54 249 to 4 772 computations (91.2% saved)

prune450.0ms (3.4%)

Memory

-8.0MiB live, 439.9MiB allocated

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	1 401	29	1 430
Fresh	15	4	19
Picked	4	1	5
Done	1	0	1
Total	1 421	34	1 455

Accuracy

100.0%

Counts

1 455 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.4%	(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	91.8%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32))) (.f32 cosTheta (fma.f32 c c #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 c cosTheta (neg.f32 cosTheta))))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (+.f32 #s(literal 1 binary32) c)))
	91.3%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	97.8%	(/.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)))
▶	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta))))))
	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))))))
	91.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (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))))
	96.2%	(/.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 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))))
	94.5%	(/.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))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.4%	(/.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 (/.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))) #s(literal 1 binary32))))
▶	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 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	97.4%	(/.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))))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	94.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	95.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))))
	94.6%	(/.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 (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)))
	96.1%	(/.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)))
	95.2%	(/.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 (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (.f32 (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) cosTheta)) (fma.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (.f32 cosTheta (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (+.f32 cosTheta (*.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (sqrt.f32 (PI.f32))))))))
	94.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) (*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta)))
	94.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))))
▶	51.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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))))))
	51.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))))
	90.8%	(.f32 (/.f32 (fma.f32 c cosTheta (neg.f32 cosTheta)) (fma.f32 (.f32 cosTheta (fma.f32 c c #s(literal -1 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 (fma.f32 c c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32)))) (.f32 (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (+.f32 c #s(literal -1 binary32)) (+.f32 c #s(literal -1 binary32)))) (/.f32 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (PI.f32) (sqrt.f32 (PI.f32))))))) (fma.f32 (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32)))) (-.f32 (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (fma.f32 c c #s(literal -1 binary32)))) (.f32 (.f32 cosTheta cosTheta) (*.f32 (fma.f32 c c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))))))
	34.2%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.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 (/.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)))))
	59.0%	(.f32 (/.f32 #s(literal 1 binary32) (-.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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
▶	90.9%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))) (sqrt.f32 (PI.f32)))))
▶	92.1%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (pow (cbrt (PI)) -3/2) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 c (fma.f32 c (-.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (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))) #s(literal 1 binary32)) #s(literal 3 binary32))) (/.f32 c (pow.f32 (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))) #s(literal 1 binary32)) #s(literal 4 binary32)))) (/.f32 #s(literal -1 binary32) (pow.f32 (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))) #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))))
	95.1%	#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)))))
✓	5.0%	#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 2 230 to 1 078 computations (51.7% saved)

simplify447.0ms (3.4%)

Memory

-2.3MiB live, 494.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	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 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
✓	cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))
✓	cost-diff	0	#s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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))))
✓	cost-diff	0	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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))))))
✓	cost-diff	1024	(.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)))
✓	cost-diff	0	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))) (sqrt.f32 (PI.f32)))))
✓	cost-diff	32	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32)))
✓	cost-diff	64	(*.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32))))
✓	cost-diff	192	(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))
✓	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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta))))))

Rules

10 108×	`lower-fma.f64`
10 098×	`lower-fma.f32`
4 378×	`lower-*.f64`
4 360×	`lower-*.f32`
2 066×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	749
0	136	749
1	256	725
2	574	717
3	1546	706
4	5527	646
0	8325	636

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

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

localize558.0ms (4.2%)

Memory

-17.8MiB live, 376.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
✓	accuracy	98.1%	(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.6%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	98.1%	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	96.5%	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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)))))
✓	accuracy	55.3%	(.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)))
✓	accuracy	97.4%	(*.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32))))
✓	accuracy	97.3%	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32)))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	95.4%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))) (sqrt.f32 (PI.f32)))))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	91.9%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	99.8%	(.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta)))
✓	accuracy	99.3%	(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta))))))
✓	accuracy	98.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Samples

448.0ms

256×

valid

Compiler

Compiled 595 to 78 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 425.0ms

ival-div: 285.0ms (67% of total)

ival-mult: 97.0ms (22.8% of total)

ival-add: 16.0ms (3.8% of total)

ival-sqrt: 10.0ms (2.4% of total)

ival-exp: 8.0ms (1.9% of total)

ival-sub: 4.0ms (0.9% of total)

ival-neg: 3.0ms (0.7% of total)

ival-pi: 1.0ms (0.2% of total)

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

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

exact: 0.0ms (0% of total)

series43.0ms (0.3%)

Memory

28.5MiB live, 104.7MiB allocated

Counts

25 → 396

Calls

Call 1

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

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

Calls

99 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))))))
3.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))))))
2.0ms	cosTheta	@	0	(* cosTheta (sqrt (PI)))
1.0ms	c	@	0	(* c (- (+ 1 (+ (/ 1 c) (/ (sqrt (/ 1 (PI))) (* cosTheta c)))) (/ (sqrt (/ 1 (PI))) c)))
1.0ms	c	@	-inf	(* c (- (+ 1 (+ (/ 1 c) (/ (sqrt (/ 1 (PI))) (* cosTheta c)))) (/ (sqrt (/ 1 (PI))) c)))

simplify614.0ms (4.6%)

Memory

3.7MiB live, 604.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6 978×	`lower-*.f64`
6 978×	`lower-*.f32`
6 450×	`lower-fma.f64`
6 450×	`lower-fma.f32`
4 452×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1171	18876
1	3888	18104
0	8564	17279

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 380

Calls

Call 1

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

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

rewrite430.0ms (3.2%)

Memory

-15.4MiB live, 618.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 640×	`lower-*.f64`
3 622×	`lower-*.f32`
3 288×	`lower-fma.f64`
3 278×	`lower-fma.f32`
2 596×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	556
0	136	555
1	587	499
2	5864	499
0	8095	492

Stop Event

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

Counts

25 → 520

Calls

Call 1

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

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

eval190.0ms (1.4%)

Memory: 28.1MiB live, 423.1MiB allocated
Compiler: Compiled 45 489 to 3 967 computations (91.3% saved)

prune188.0ms (1.4%)

Memory

-11.9MiB live, 594.4MiB allocated

Pruning

35 alts after pruning (33 fresh and 2 done)

	Pruned	Kept	Total
New	1 211	17	1 228
Fresh	12	16	28
Picked	4	1	5
Done	0	1	1
Total	1 227	35	1 262

Accuracy

100.0%

Counts

1 262 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.4%	(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	91.8%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32))) (.f32 cosTheta (fma.f32 c c #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 c cosTheta (neg.f32 cosTheta))))
	91.3%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))))
▶	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	91.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	94.5%	(/.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))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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))))
	97.4%	(/.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 (/.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))) #s(literal 1 binary32))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	94.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	95.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))))
▶	94.6%	(/.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 (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)))
	96.1%	(/.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)))
	94.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) (*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta)))
	51.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 c (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c (sqrt.f32 (PI.f32))))) (-.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (.f32 c (sqrt.f32 (PI.f32)))))) c)))))
	51.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.f32 c (-.f32 (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 cosTheta c)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))))
▶	51.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c)))))))
	34.2%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.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 (/.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)))))
	34.9%	(.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)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta)) #s(literal 3 binary32)))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.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 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta)) (+.f32 #s(literal 1 binary32) c)) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
	59.0%	(.f32 (/.f32 #s(literal 1 binary32) (-.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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	90.9%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (fma.f32 (PI.f32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))
▶	92.1%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))))
	92.2%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 3/2 binary32))))
	90.2%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
✓	92.1%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
	95.1%	#s(approx (/ 1 (+ (+ 1 c) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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)))))
✓	5.0%	#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 1 939 to 1 011 computations (47.9% saved)

simplify333.0ms (2.5%)

Memory

-4.6MiB live, 673.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(+.f32 cosTheta (*.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
✓	cost-diff	64	(fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	224	(/.f32 (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)
✓	cost-diff	576	(fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	#s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c)))))
✓	cost-diff	0	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c)))))))
✓	cost-diff	576	(.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))))
✓	cost-diff	0	(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* 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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
✓	cost-diff	0	#s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c)))
✓	cost-diff	0	(fma.f32 cosTheta #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))))
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
✓	cost-diff	160	(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
✓	cost-diff	480	(fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32))))

Rules

8 722×	`lower-fma.f64`
8 708×	`lower-fma.f32`
3 766×	`lower-+.f64`
3 750×	`lower-+.f32`
3 748×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	1166
0	166	1160
1	346	1128
2	874	1115
3	2975	1087
4	5692	1077
0	8785	1025

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

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

localize300.0ms (2.3%)

Memory

-1.8MiB live, 632.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	97.7%	(/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	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	96.5%	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta))
✓	accuracy	98.9%	(*.f32 (sqrt.f32 (PI.f32)) c)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	96.5%	#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))))))
✓	accuracy	55.3%	(.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))))
✓	accuracy	99.3%	(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
✓	accuracy	98.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	96.6%	#s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	99.0%	(*.f32 (PI.f32) (neg.f32 c))
✓	accuracy	98.9%	(.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32))))
✓	accuracy	95.4%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))))
✓	accuracy	7.6%	#s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c)))
✓	accuracy	99.3%	(.f32 (.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))
✓	accuracy	99.3%	(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
✓	accuracy	98.8%	(.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))

Samples

158.0ms

256×

valid

Compiler

Compiled 825 to 97 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-mult: 43.0ms (32.9% of total)

ival-div: 32.0ms (24.5% of total)

ival-add: 26.0ms (19.9% of total)

ival-sqrt: 8.0ms (6.1% of total)

ival-exp: 6.0ms (4.6% of total)

const: 5.0ms (3.8% of total)

ival-neg: 5.0ms (3.8% of total)

ival-sub: 4.0ms (3.1% of total)

ival-pi: 1.0ms (0.8% of total)

exact: 1.0ms (0.8% of total)

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

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

series74.0ms (0.6%)

Memory

14.3MiB live, 92.8MiB allocated

Counts

32 → 564

Calls

Call 1

Inputs
#<alt (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32))))>
#<alt (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))>
#<alt (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))))>
#<alt #s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))))>
#<alt (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32))))>
#<alt (fma.f32 cosTheta #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))>
#<alt #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c)))>
#<alt (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))>
#<alt (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))>
#<alt (+.f32 #s(literal 1 binary32) c)>
#<alt (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))>
#<alt (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))))>
#<alt (/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c)))))))>
#<alt #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))))))>
#<alt #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c)))))>
#<alt (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))>
#<alt (/.f32 (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)>
#<alt (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))>
#<alt (+.f32 cosTheta (*.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))>
#<alt (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))>
#<alt (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32) (.f32 (.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))>
#<alt (.f32 (.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))>
#<alt (*.f32 (PI.f32) (neg.f32 c))>
#<alt #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))>
#<alt (*.f32 cosTheta (sqrt.f32 (PI.f32)))>
#<alt (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))>
#<alt (*.f32 (sqrt.f32 (PI.f32)) c)>
#<alt #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta))>
#<alt (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))>
#<alt (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))>
#<alt (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))>

Outputs
#<alt (* 1/2 (sqrt (PI)))>
#<alt (+ (* 1/6 (* (pow cosTheta 2) (sqrt (PI)))) (* 1/2 (sqrt (PI))))>
#<alt (+ (* 1/6 (* (pow cosTheta 2) (sqrt (PI)))) (* 1/2 (sqrt (PI))))>
#<alt (+ (* 1/6 (* (pow cosTheta 2) (sqrt (PI)))) (* 1/2 (sqrt (PI))))>
#<alt (* 1/6 (* (pow cosTheta 2) (sqrt (PI))))>
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#<alt (* c (sqrt (PI)))>
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#<alt (/ (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))>
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#<alt (- (+ (* c (- (+ (* c (- (+ (* -1 (/ (* c (* cosTheta (- (/ (pow cosTheta 2) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (/ (* cosTheta (- (/ (* cosTheta (+ cosTheta (+ (* -1 (* cosTheta (sqrt (/ 1 (PI))))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (/ (* cosTheta (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI)))) (pow (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) 2)))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (/ (pow cosTheta 2) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (/ (* cosTheta (- (/ (* cosTheta (+ cosTheta (+ (* -1 (* cosTheta (sqrt (/ 1 (PI))))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (/ (* cosTheta (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI)))) (pow (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) 2)))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))))) (/ (* cosTheta (+ cosTheta (+ (* -1 (* cosTheta (sqrt (/ 1 (PI))))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (/ (* cosTheta (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI)))) (pow (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) 2)))) (/ (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (/ 1 (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* c cosTheta)>
#<alt (* c (- (+ cosTheta (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (/ cosTheta c))) (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))>
#<alt (* c (- (+ cosTheta (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (+ (/ cosTheta c) (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) (pow c 2))))) (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow c 2) (* cosTheta (PI)))) (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) (* -1 (sqrt (/ 1 (PI)))))) (* (pow c 2) cosTheta))))))>
#<alt (* c (- (+ cosTheta (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) (+ (/ 1 (* cosTheta (PI))) (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) (* -1 (sqrt (/ 1 (PI)))))) cosTheta)))) (* (pow c 3) cosTheta))) (+ (/ cosTheta c) (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))) (pow c 2)))))) (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow c 2) (* cosTheta (PI)))) (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) (* -1 (sqrt (/ 1 (PI)))))) (* (pow c 2) cosTheta))))))>
#<alt (* c cosTheta)>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (- (* -1 (+ (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) c)))))>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (- (+ (* -1 (+ (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))) (* -1 (/ (- (* -1 (/ (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI))) cosTheta)) (* -1 (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (* -1 (+ (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) cosTheta))) c))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) c)))))>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (- (+ (* -1 (+ (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))) (* -1 (/ (- (+ (* -1 (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (* -1 (/ (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI))) cosTheta)) (* -1 (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (* -1 (+ (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)))) (* c cosTheta))) (* -1 (/ (- (* cosTheta (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI)))))))) (/ 1 (PI))) cosTheta))) (* -1 (/ (* (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (- (* -1 (+ (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (+ cosTheta (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) cosTheta))) c))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) c)))))>

Calls

141 calls:

Time	Variable		Point	Expression
12.0ms	c	@	0	(* (PI) (neg c))
8.0ms	c	@	0	(/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta)
1.0ms	c	@	-inf	(/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta)
1.0ms	cosTheta	@	0	(* cosTheta (+ (* cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI))))
1.0ms	cosTheta	@	-inf	(/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta)

simplify438.0ms (3.3%)

Memory

-6.2MiB live, 585.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 304×	`lower-*.f64`
6 304×	`lower-*.f32`
5 010×	`lower-fma.f64`
5 010×	`lower-fma.f32`
3 648×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1599	22930
1	5561	21717
0	8340	20980

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 546

Calls

Call 1

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

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

rewrite372.0ms (2.8%)

Memory

3.4MiB live, 477.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 922×	`lower-fma.f64`
4 908×	`lower-fma.f32`
4 230×	`lower-*.f64`
4 206×	`lower-*.f32`
3 332×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	869
0	164	841
1	767	725
2	7713	725
0	8052	703

Stop Event

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

Counts

32 → 619

Calls

Call 1

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

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

eval155.0ms (1.2%)

Memory: 12.5MiB live, 316.7MiB allocated
Compiler: Compiled 63 964 to 4 895 computations (92.3% saved)

prune432.0ms (3.3%)

Memory

-135.8MiB live, 419.9MiB allocated

Pruning

40 alts after pruning (36 fresh and 4 done)

	Pruned	Kept	Total
New	1 280	18	1 298
Fresh	10	18	28
Picked	3	2	5
Done	0	2	2
Total	1 293	40	1 333

Accuracy

100.0%

Counts

1 333 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.4%	(pow.f32 (pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) c)))
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) c)))
	55.9%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
	91.3%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))) (+.f32 #s(literal 1 binary32) c)))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(approx (+ ( (sqrt (PI)) 1/2) (* (* 1/6 (* cosTheta cosTheta)) (sqrt (PI)))) (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32))))))))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))))
✓	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	91.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	94.5%	(/.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))))
	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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))))
	97.4%	(/.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 (/.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))) #s(literal 1 binary32))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(approx (+ 1 c) #s(literal 1 binary32)))))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	94.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
	96.1%	(/.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)))
	94.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) (+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)))
	94.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))))
	51.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.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)))) c)) #s(literal -1 binary32))))))
	94.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) #s(approx (* c (- (+ 1 (+ (/ 1 c) (/ (sqrt (/ 1 (PI))) (* cosTheta c)))) (/ 1 (* (sqrt (PI)) c)))) (+.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))))))))
	56.0%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))))
	34.8%	(.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)) (pow.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))) #s(literal 3 binary32)))) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))) (-.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
	31.9%	(.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 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx ( (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
	59.0%	(.f32 (/.f32 #s(literal 1 binary32) (-.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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	92.6%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (/.f32 (.f32 (fma.f32 #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) cosTheta) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (sqrt.f32 (PI.f32))))))
	90.9%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (fma.f32 (PI.f32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))
✓	92.1%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (sqrt.f32 (PI.f32)))))
	92.3%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (fma.f32 #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (sqrt.f32 (PI.f32))))))))
	90.2%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
✓	92.1%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
	90.8%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta #s(approx (+ ( cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI))) (.f32 (neg.f32 c) (-.f32 (.f32 (PI.f32) cosTheta) (/.f32 (-.f32 (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)) (sqrt.f32 (PI.f32))) (*.f32 (PI.f32) cosTheta)) c))))))
	90.8%	#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) #s(approx (* cosTheta (+ (* cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI)))) (.f32 c (fma.f32 cosTheta (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (PI.f32) cosTheta))) c) (neg.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))))
	95.1%	#s(approx (/ 1 (+ (+ 1 c) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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)))))
✓	5.0%	#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 3 898 to 1 061 computations (72.8% saved)

regimes161.0ms (1.2%)

Memory

31.2MiB live, 294.9MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

30.0ms	c
25.0ms	(.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)))
25.0ms	(+.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))))
25.0ms	cosTheta
25.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta`
98.3%	1	`c`
98.3%	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)))))`
98.3%	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))))`
98.3%	1	`(+.f32 #s(literal 1 binary32) c)`
98.3%	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)

regimes117.0ms (0.9%)

Memory

-30.4MiB live, 206.9MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

26.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
18.0ms	c
18.0ms	(/.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)))))
17.0ms	(.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)))
16.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta`
98.3%	1	`c`
98.3%	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)))))`
98.3%	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))))`
98.3%	1	`(+.f32 #s(literal 1 binary32) c)`
98.3%	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)

regimes110.0ms (0.8%)

Memory

20.8MiB live, 212.8MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

21.0ms	c
18.0ms	(/.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)))))
18.0ms	(+.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))))
18.0ms	(.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)))
16.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.1%	1	`c`
98.1%	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))))`
98.1%	1	`(+.f32 #s(literal 1 binary32) c)`
98.1%	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)))`
98.1%	1	`cosTheta`
98.1%	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)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes118.0ms (0.9%)

Memory

2.5MiB live, 202.3MiB allocated

Counts

47 → 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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (fma.f32 (PI.f32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))
#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) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) #s(approx (* c (- (+ 1 (+ (/ 1 c) (/ (sqrt (/ 1 (PI))) (* cosTheta c)))) (/ 1 (* (sqrt (PI)) c)))) (+.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))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta 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 (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) 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) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 #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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta #s(approx (+ ( cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI))) (.f32 (neg.f32 c) (-.f32 (.f32 (PI.f32) cosTheta) (/.f32 (-.f32 (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)) (sqrt.f32 (PI.f32))) (*.f32 (PI.f32) cosTheta)) c))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) #s(approx (* cosTheta (+ (* cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI)))) (.f32 c (fma.f32 cosTheta (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (PI.f32) cosTheta))) c) (neg.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (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 #s(approx (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) (+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (/.f32 (.f32 (fma.f32 #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) cosTheta) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (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 (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)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.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)))) c)) #s(literal -1 binary32))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (fma.f32 #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (sqrt.f32 (PI.f32))))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))) (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) 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) (* (* (/ 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 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #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 (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) 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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 c (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c (sqrt.f32 (PI.f32))))) (-.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (.f32 c (sqrt.f32 (PI.f32)))))) 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 (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) 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 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) (*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(approx (+ ( (sqrt (PI)) 1/2) (* (* 1/6 (* cosTheta cosTheta)) (sqrt (PI)))) (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (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 (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 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal 1/6 binary32) (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))) (+.f32 #s(literal 1 binary32) c)))

Outputs

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

Calls

6 calls:

22.0ms	(+.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))))
21.0ms	c
21.0ms	cosTheta
19.0ms	(+.f32 #s(literal 1 binary32) c)
18.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.1%	1	`c`
98.1%	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))))`
98.1%	1	`(+.f32 #s(literal 1 binary32) c)`
98.1%	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)))`
98.1%	1	`cosTheta`
98.1%	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)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes111.0ms (0.8%)

Memory

-0.0MiB live, 172.6MiB allocated

Counts

46 → 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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (fma.f32 (PI.f32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))
#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) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) #s(approx (* c (- (+ 1 (+ (/ 1 c) (/ (sqrt (/ 1 (PI))) (* cosTheta c)))) (/ 1 (* (sqrt (PI)) c)))) (+.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))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta 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 (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) 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) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 #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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta #s(approx (+ ( cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI))) (.f32 (neg.f32 c) (-.f32 (.f32 (PI.f32) cosTheta) (/.f32 (-.f32 (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)) (sqrt.f32 (PI.f32))) (*.f32 (PI.f32) cosTheta)) c))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) #s(approx (* cosTheta (+ (* cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI)))) (.f32 c (fma.f32 cosTheta (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (PI.f32) cosTheta))) c) (neg.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (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 #s(approx (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) (+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (/.f32 (.f32 (fma.f32 #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) cosTheta) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (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 (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)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.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)))) c)) #s(literal -1 binary32))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (fma.f32 #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (sqrt.f32 (PI.f32))))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))) (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) 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) (* (* (/ 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 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #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 (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) 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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 c (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c (sqrt.f32 (PI.f32))))) (-.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (.f32 c (sqrt.f32 (PI.f32)))))) 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 (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) 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 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) (*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(approx (+ ( (sqrt (PI)) 1/2) (* (* 1/6 (* cosTheta cosTheta)) (sqrt (PI)))) (*.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (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 (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

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

Calls

6 calls:

24.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
21.0ms	c
20.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
13.0ms	(+.f32 (+.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

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes103.0ms (0.8%)

Memory

-28.7MiB live, 132.7MiB allocated

Counts

43 → 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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (fma.f32 (PI.f32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))))
#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) (/ (sqrt (+ (* cosTheta -2) 1)) (* (* cosTheta (sqrt (PI))) (exp (* 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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) #s(approx (* c (- (+ 1 (+ (/ 1 c) (/ (sqrt (/ 1 (PI))) (* cosTheta c)))) (/ 1 (* (sqrt (PI)) c)))) (+.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))))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) cosTheta) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta 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 (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) 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) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 #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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta #s(approx (+ ( cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI))) (.f32 (neg.f32 c) (-.f32 (.f32 (PI.f32) cosTheta) (/.f32 (-.f32 (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)) (sqrt.f32 (PI.f32))) (*.f32 (PI.f32) cosTheta)) c))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) #s(approx (* cosTheta (+ (* cosTheta (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1)))) (sqrt (PI)))) (.f32 c (fma.f32 cosTheta (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (PI.f32) cosTheta))) c) (neg.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(approx (* (* cosTheta (sqrt (PI))) (exp (* cosTheta cosTheta))) (.f32 cosTheta (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (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 #s(approx (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))) (+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (/.f32 (.f32 (fma.f32 #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) cosTheta) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (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 (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)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.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)))) c)) #s(literal -1 binary32))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (.f32 (fma.f32 #s(approx (* (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c))) (.f32 (.f32 cosTheta cosTheta) #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (.f32 (PI.f32) (neg.f32 c)))) (neg.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(approx ( (neg (PI)) (/ (+ (* (sqrt (/ 1 (PI))) (+ c -1)) (+ (* c c) -1)) (+ c -1))) (*.f32 (PI.f32) (neg.f32 c))) (neg.f32 (sqrt.f32 (PI.f32))))))))
#s(approx (/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (.f32 cosTheta (fma.f32 cosTheta (.f32 (neg.f32 (PI.f32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal -1 binary32)))) (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) 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) (* (* (/ 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 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #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 (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)))) (fma.f32 #s(approx (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) 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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 c (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c (sqrt.f32 (PI.f32))))) (-.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (.f32 c (sqrt.f32 (PI.f32)))))) 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 (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) 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 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) (*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta) (.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))))))

Outputs

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

Calls

6 calls:

31.0ms	(/.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	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
15.0ms	(+.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	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes67.0ms (0.5%)

Memory

5.2MiB live, 125.2MiB allocated

Counts

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

Calls

6 calls:

12.0ms	cosTheta
11.0ms	(/.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)))))
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)))
10.0ms	(+.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))))
10.0ms	c

Results

Accuracy	Segments	Branch
97.4%	1	`cosTheta`
97.4%	1	`c`
97.4%	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)))))`
97.4%	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))))`
97.4%	1	`(+.f32 #s(literal 1 binary32) c)`
97.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes99.0ms (0.7%)

Memory

8.9MiB live, 84.5MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

36.0ms	(+.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))))
25.0ms	cosTheta
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	c

Results

Accuracy	Segments	Branch
97.4%	1	`cosTheta`
97.4%	1	`c`
97.4%	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)))))`
97.4%	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))))`
97.4%	1	`(+.f32 #s(literal 1 binary32) c)`
97.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes50.0ms (0.4%)

Memory

-2.6MiB live, 79.5MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

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))))
9.0ms	c
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
7.0ms	(/.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)))))
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.9%	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))))`
96.9%	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)))`
96.9%	1	`cosTheta`
96.9%	1	`c`
96.9%	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)))))`
96.9%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes45.0ms (0.3%)

Memory

5.8MiB live, 78.8MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

9.0ms	cosTheta
9.0ms	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)))
7.0ms	(+.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))))
7.0ms	(/.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
95.2%	1	`cosTheta`
95.2%	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)))))`
95.2%	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))))`
95.2%	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)))`
95.2%	1	`c`
95.2%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes86.0ms (0.6%)

Memory

-45.8MiB live, 74.3MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

34.0ms	cosTheta
24.0ms	(+.f32 #s(literal 1 binary32) 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)))
7.0ms	(/.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)))))
7.0ms	(+.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
95.2%	1	`cosTheta`
95.2%	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)))))`
95.2%	1	`c`
95.2%	1	`(+.f32 #s(literal 1 binary32) c)`
95.2%	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))))`
95.2%	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)

regimes38.0ms (0.3%)

Memory

38.5MiB live, 76.7MiB allocated

Counts

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

7.0ms	c
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	(.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
95.1%	1	`cosTheta`
95.1%	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)))))`
95.1%	1	`c`
95.1%	1	`(+.f32 #s(literal 1 binary32) c)`
95.1%	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))))`
95.1%	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)

regimes26.0ms (0.2%)

Memory

-21.9MiB live, 54.3MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

5.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
5.0ms	c
4.0ms	(/.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	cosTheta

Results

Accuracy	Segments	Branch
92.1%	1	`(+.f32 #s(literal 1 binary32) c)`
92.1%	1	`c`
92.1%	1	`cosTheta`
92.1%	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)))))`
92.1%	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))))`
92.1%	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)

regimes15.0ms (0.1%)

Memory

-11.6MiB live, 30.3MiB allocated

Counts

3 → 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 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (+ 1 (+ cosTheta cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))))) (* (+ c -1) cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))

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

Results

Accuracy	Segments	Branch
92.1%	1	`(+.f32 #s(literal 1 binary32) c)`
92.1%	1	`cosTheta`
92.1%	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)))))`
92.1%	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))))`
92.1%	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)))`
92.1%	1	`c`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes8.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB 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	(+.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 #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 (/.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
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
5.0%	1	`cosTheta`
5.0%	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)))))`
5.0%	1	`(+.f32 #s(literal 1 binary32) c)`
5.0%	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))))`
5.0%	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)))`
5.0%	1	`c`

Compiler

Compiled 84 to 58 computations (31% saved)

simplify14.0ms (0.1%)

Memory

-9.9MiB live, 29.5MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary32`
26×	`+-commutative_binary32`
12×	`sub-neg_binary32`
10×	`neg-sub0_binary32`
10×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	598
1	179	598
2	192	598
3	201	598
4	205	598
5	206	598

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.4s (10.2%)

Memory

16.7MiB live, 1 251.4MiB allocated

Rules

9 656×	`lower-fma.f64`
9 656×	`lower-fma.f32`
6 978×	`lower-*.f64`
6 978×	`lower-*.f32`
6 838×	`lower-*.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	869
0	164	841
1	767	725
2	7713	725
0	8052	703
0	18	89
0	33	89
1	141	80
2	1060	73
0	8552	73
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311
0	1094	20423
1	3658	19698
0	8099	18799
0	69	484
0	119	485
1	460	418
2	3823	398
0	8301	398
0	1171	18876
1	3888	18104
0	8564	17279

Stop Event

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

Compiler

Compiled 1 006 to 432 computations (57.1% saved)

preprocess90.0ms (0.7%)

Memory: 10.8MiB live, 165.9MiB allocated
Compiler: Compiled 706 to 206 computations (70.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze143.0ms (1.1%)

sample1.9s (14.1%)

preprocess227.0ms (1.7%)

explain257.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify189.0ms (1.4%)

localize98.0ms (0.7%)

series24.0ms (0.2%)

simplify432.0ms (3.3%)

rewrite366.0ms (2.8%)

eval92.0ms (0.7%)

prune151.0ms (1.1%)

simplify302.0ms (2.3%)

localize227.0ms (1.7%)

series199.0ms (1.5%)

simplify384.0ms (2.9%)

rewrite382.0ms (2.9%)

eval252.0ms (1.9%)

prune450.0ms (3.4%)

simplify447.0ms (3.4%)

localize558.0ms (4.2%)

series43.0ms (0.3%)

simplify614.0ms (4.6%)

rewrite430.0ms (3.2%)

eval190.0ms (1.4%)

prune188.0ms (1.4%)

simplify333.0ms (2.5%)

localize300.0ms (2.3%)

series74.0ms (0.6%)

simplify438.0ms (3.3%)

rewrite372.0ms (2.8%)

eval155.0ms (1.2%)

prune432.0ms (3.3%)

regimes161.0ms (1.2%)

regimes117.0ms (0.9%)

regimes110.0ms (0.8%)

regimes118.0ms (0.9%)

regimes111.0ms (0.8%)

regimes103.0ms (0.8%)

regimes67.0ms (0.5%)

regimes99.0ms (0.7%)

regimes50.0ms (0.4%)

regimes45.0ms (0.3%)

regimes86.0ms (0.6%)

regimes38.0ms (0.3%)

regimes26.0ms (0.2%)

regimes15.0ms (0.1%)

regimes8.0ms (0.1%)

simplify14.0ms (0.1%)

soundness1.4s (10.2%)

preprocess90.0ms (0.7%)

end0.0ms (0%)

Profiling