Metrics for Beckmann Sample, normalization factor

analyze37.0ms (0.3%)

Memory

-8.9MiB live, 87.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.2s (16.3%)

Memory

28.0MiB live, 2 941.6MiB allocated

Samples

1.7s	8 256×	0	valid
36.0ms	72×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

const: 219.0ms (16.1% of total)

ival-div: 209.0ms (15.4% of total)

ival-mult: 199.0ms (14.6% of total)

ival-sqrt: 152.0ms (11.2% of total)

ival-add: 148.0ms (10.9% of total)

ival-<: 113.0ms (8.3% of total)

ival-sub: 101.0ms (7.4% of total)

ival-exp: 93.0ms (6.8% of total)

ival-neg: 55.0ms (4% of total)

ival-pi: 30.0ms (2.2% of total)

ival-and: 22.0ms (1.6% of total)

exact: 15.0ms (1.1% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

preprocess241.0ms (1.8%)

Memory

29.3MiB live, 151.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

explain322.0ms (2.3%)

Memory

-24.8MiB live, 218.1MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

73.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-div: 21.0ms (38.2% of total)

ival-mult: 9.0ms (16.4% of total)

ival-sqrt: 7.0ms (12.7% of total)

ival-add: 5.0ms (9.1% of total)

ival-sub: 5.0ms (9.1% of total)

ival-exp: 4.0ms (7.3% of total)

ival-pi: 2.0ms (3.6% of total)

ival-neg: 2.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

97.9%

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

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify203.0ms (1.5%)

Memory

18.5MiB live, 96.4MiB 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)

localize139.0ms (1%)

Memory

-21.3MiB live, 95.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.0%	(/.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)))))
✓	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

63.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-add: 34.0ms (63.6% of total)

ival-div: 5.0ms (9.3% of total)

ival-mult: 4.0ms (7.5% of total)

ival-sqrt: 3.0ms (5.6% of total)

ival-exp: 2.0ms (3.7% of total)

ival-sub: 2.0ms (3.7% of total)

ival-pi: 1.0ms (1.9% of total)

ival-neg: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series32.0ms (0.2%)

Memory

1.0MiB live, 36.6MiB allocated

Counts

6 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite432.0ms (3.1%)

Memory

25.6MiB live, 379.2MiB 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))
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(/.f32 (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (pow.f32 (neg.f32 (.f32 cosTheta cosTheta)) #s(literal 3 binary32))) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (-.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 (fma.f32 cosTheta (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))) (fma.f32 cosTheta cosTheta (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (*.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 3 binary32)) (pow.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (*.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))))
(/.f32 (-.f32 (pow.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta) (.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (neg.f32 (.f32 cosTheta cosTheta)))) (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 (.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (.f32 cosTheta cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 (neg.f32 cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (+.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(*.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))
(*.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 4 binary32) (.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta)))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (fma.f32 cosTheta cosTheta (*.f32 (neg.f32 (-.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(*.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) #s(literal -1 binary32))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) (fma.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta cosTheta)) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta cosTheta))))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal 4 binary32) (*.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))

simplify473.0ms (3.4%)

Memory

-9.7MiB live, 699.8MiB 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)
(/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32)) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(neg.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
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c
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))) (+.f32 #s(literal 1 binary32) c))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32)) c)))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) #s(literal 1/2 binary32)) c))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32)) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))))) (+.f32 #s(literal 1 binary32) c))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 binary32)) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c)))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
(+.f32 (+.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c)) (fma.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/8 binary32) (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))
(+.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 binary32)) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) #s(literal -1/16 binary32))))))
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(+ 1 (* -2 cosTheta))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* cosTheta (- (/ 1 cosTheta) 2))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))

eval73.0ms (0.5%)

Memory: 8.3MiB live, 202.8MiB allocated
Compiler: Compiled 23 190 to 2 839 computations (87.8% saved)

prune140.0ms (1%)

Memory

-33.1MiB live, 294.9MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	528	27	555
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	529	27	556

Accuracy

99.8%

Counts

556 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	91.2%	(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))
	46.9%	(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (*.f32 cosTheta cosTheta))))))))
▶	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	60.3%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	91.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c (.f32 c c) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (fma.f32 c (+.f32 c #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (*.f32 (fma.f32 c (+.f32 c #s(literal -1 binary32)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
▶	91.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	91.4%	(/.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)))
▶	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	96.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	92.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	91.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
▶	91.9%	(/.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))))
	92.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	91.8%	(/.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)))))
▶	5.0%	(/.f32 #s(literal 1 binary32) c)
	46.8%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (neg.f32 (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (.f32 cosTheta cosTheta)))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))))
	28.2%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta))) (exp.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) #s(literal -1 binary32)))
	96.0%	(*.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%	(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (.f32 (-.f32 (+.f32 #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))))
	92.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	84.0%	(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))

Compiler

Compiled 1 634 to 880 computations (46.1% saved)

simplify368.0ms (2.7%)

Memory

4.9MiB live, 798.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
✓	cost-diff	96	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
✓	cost-diff	512	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.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)))
✓	cost-diff	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))))
✓	cost-diff	64	(/.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))
✓	cost-diff	0	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	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	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
✓	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	(exp.f32 (*.f32 cosTheta (neg.f32 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	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))

Rules

13 558×	`lower-fma.f64`
13 548×	`lower-fma.f32`
3 600×	`lower-+.f64`
3 590×	`lower-+.f32`
2 418×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	449
0	86	449
1	151	449
2	281	435
3	651	435
4	1570	421
5	3369	419
6	7175	419
0	8066	396

Stop Event

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

Calls

Call 1

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

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

localize218.0ms (1.6%)

Memory

-3.2MiB live, 513.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta)
✓	accuracy	99.7%	(*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.9%	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
✓	accuracy	99.9%	(.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))
✓	accuracy	99.0%	(/.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))
✓	accuracy	99.0%	(/.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))))
✓	accuracy	98.8%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
✓	accuracy	98.3%	(/.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	97.0%	(-.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	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.9%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.2%	(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	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))

Samples

86.0ms

256×

valid

Compiler

Compiled 468 to 50 computations (89.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-div: 21.0ms (32.4% of total)

ival-mult: 16.0ms (24.7% of total)

ival-add: 11.0ms (17% of total)

ival-sqrt: 7.0ms (10.8% of total)

ival-exp: 4.0ms (6.2% of total)

ival-neg: 4.0ms (6.2% of total)

ival-pi: 1.0ms (1.5% of total)

ival-sub: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series92.0ms (0.7%)

Memory

15.3MiB live, 210.6MiB allocated

Counts

23 → 384

Calls

Call 1

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

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

Calls

96 calls:

Time	Variable		Point	Expression
10.0ms	cosTheta	@	inf	(/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (+ c -1) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))) (* (+ c -1) (sqrt (PI))))
5.0ms	cosTheta	@	-inf	(/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (+ c -1) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))) (* (+ c -1) (sqrt (PI)))))
4.0ms	cosTheta	@	inf	(/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (+ c -1) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))) (* (+ c -1) (sqrt (PI)))))
4.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) (* (sqrt (PI)) cosTheta))))
4.0ms	c	@	0	(/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (+ c -1) (/ (* (sqrt (+ 1 (+ cosTheta cosTheta))) (exp (neg (* cosTheta cosTheta)))) cosTheta))) (* (+ c -1) (sqrt (PI))))

rewrite256.0ms (1.9%)

Memory

-1.7MiB live, 559.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 730×	`lower-/.f64`
2 712×	`lower-/.f32`
2 700×	`lower-*.f64`
2 688×	`lower-*.f32`
2 146×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	317
0	86	300
1	361	285
2	3098	234
0	9127	234

Stop Event

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

Counts

23 → 869

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 #s(literal -1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
(pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal -1 binary32))
(pow.f32 (neg.f32 (neg.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) #s(literal -1 binary32))
(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal -1/2 binary32))
(pow.f32 (exp.f32 (log1p.f32 (+.f32 c (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (neg.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))))
(.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))))
(.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal -1/2 binary32)) (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal -1/2 binary32)))
(.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 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -3 binary32)))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32))))
(.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 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -3 binary32)))) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))
(.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 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -3 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32)))) #s(literal -1 binary32)))
(.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 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -3 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
(exp.f32 (neg.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32))))
(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
(+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))
(+.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(+.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) c)
(+.f32 (+.f32 c (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))
(pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 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 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -3 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (-.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)) (-.f32 (pow.f32 (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (neg.f32 (.f32 cosTheta (neg.f32 cosTheta))))) #s(literal -2 binary32)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) #s(literal -1 binary32))
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(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (sqrt.f32 (*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 #s(literal -1 binary32)))
(/.f32 (neg.f32 (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 (neg.f32 (PI.f32)))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal -1 binary32) (PI.f32))))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
(exp.f32 (.f32 (log.f32 (exp.f32 (.f32 cosTheta cosTheta))) #s(literal -1 binary32)))
(exp.f32 (*.f32 (log.f32 (exp.f32 (neg.f32 cosTheta))) cosTheta))
(exp.f32 (.f32 (log.f32 (exp.f32 #s(literal -1 binary32))) (.f32 cosTheta cosTheta)))
(exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32)))
(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
(pow.f32 (exp.f32 cosTheta) (+.f32 (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32)) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32))))
(pow.f32 (exp.f32 (*.f32 cosTheta cosTheta)) #s(literal -1 binary32))
(pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta)
(pow.f32 (exp.f32 #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(pow.f32 (/.f32 (exp.f32 (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (exp.f32 (*.f32 cosTheta (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32)))) #s(literal 2 binary32))
(pow.f32 (*.f32 (exp.f32 cosTheta) (exp.f32 cosTheta)) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32)))
(/.f32 #s(literal 1 binary32) (exp.f32 (*.f32 cosTheta cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (*.f32 cosTheta cosTheta)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (exp.f32 (*.f32 cosTheta cosTheta)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (exp.f32 (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (exp.f32 (*.f32 cosTheta cosTheta)) #s(literal 1 binary32))))
(.f32 #s(literal 1 binary32) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))
(.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) #s(literal 1 binary32))
(.f32 (exp.f32 (.f32 cosTheta (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32)))) (exp.f32 (*.f32 cosTheta (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32)))))
(+.f32 (.f32 (sqrt.f32 (PI.f32)) c) (.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)))
(+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) (.f32 (sqrt.f32 (PI.f32)) c))
(+.f32 (.f32 c (sqrt.f32 (PI.f32))) (.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(+.f32 (.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (.f32 c (sqrt.f32 (PI.f32))))
(fma.f32 c (sqrt.f32 (PI.f32)) (*.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(fma.f32 (sqrt.f32 (PI.f32)) c (*.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32)))
(fma.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32) (*.f32 (sqrt.f32 (PI.f32)) c))
(fma.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)) (*.f32 c (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (sqrt.f32 (PI.f32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c))
(/.f32 (neg.f32 (*.f32 (sqrt.f32 (PI.f32)) (fma.f32 c c #s(literal -1 binary32)))) (neg.f32 (+.f32 #s(literal 1 binary32) c)))
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (fma.f32 c (.f32 c c) #s(literal -1 binary32))) (fma.f32 c c (+.f32 #s(literal 1 binary32) c)))
(/.f32 (.f32 (fma.f32 c (.f32 c c) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (fma.f32 c c (+.f32 #s(literal 1 binary32) c)))
(/.f32 (neg.f32 (.f32 (sqrt.f32 (PI.f32)) (fma.f32 c (.f32 c c) #s(literal -1 binary32)))) (neg.f32 (fma.f32 c c (+.f32 #s(literal 1 binary32) c))))
(/.f32 (neg.f32 (.f32 (fma.f32 c (.f32 c c) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 (fma.f32 c c (+.f32 #s(literal 1 binary32) c))))
(*.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal -1 binary32)))
(*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))

simplify537.0ms (3.9%)

Memory

18.8MiB live, 817.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 286×	`lower-*.f64`
7 286×	`lower-*.f32`
6 574×	`lower-fma.f64`
6 574×	`lower-fma.f32`
4 274×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1418	15236
1	4803	14772
0	8939	14075

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 372

Calls

Call 1

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

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

eval186.0ms (1.4%)

Memory: -0.1MiB live, 253.4MiB allocated
Compiler: Compiled 48 695 to 4 357 computations (91.1% saved)

prune210.0ms (1.5%)

Memory

-12.8MiB live, 358.1MiB allocated

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	1 381	16	1 397
Fresh	12	10	22
Picked	4	1	5
Done	0	0	0
Total	1 397	27	1 424

Accuracy

100.0%

Counts

1 424 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	91.8%	(pow.f32 (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	96.0%	(/.f32 (/.f32 #s(literal 1 binary32) (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) cosTheta))
	95.1%	(/.f32 cosTheta (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)))))
▶	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
▶	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	97.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	60.3%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	92.3%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	96.1%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (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)))))))
▶	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	96.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	92.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	92.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
✓	5.0%	(/.f32 #s(literal 1 binary32) c)
▶	96.4%	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (*.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (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)))))
	96.0%	(*.f32 (/.f32 #s(literal 1 binary32) (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)
	92.4%	(.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (sqrt.f32 (PI.f32)) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 c #s(literal -1 binary32)) (*.f32 (sqrt.f32 (PI.f32)) (fma.f32 c c #s(literal -1 binary32))))))
	96.0%	(*.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))))
	92.0%	(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
	97.2%	(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (.f32 (-.f32 (+.f32 #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))))
▶	92.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 235 to 722 computations (41.5% saved)

simplify426.0ms (3.1%)

Memory

41.1MiB live, 671.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (*.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (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)))))
✓	cost-diff	64	(neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	128	(fma.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	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	(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))
✓	cost-diff	0	(/.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)
✓	cost-diff	0	(fma.f32 (/.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))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
✓	cost-diff	0	(+.f32 c #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
✓	cost-diff	544	(/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
✓	cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(fma.f32 (.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))
✓	cost-diff	0	(/.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)
✓	cost-diff	0	(fma.f32 (/.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))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))

Rules

18 890×	`lower-fma.f64`
18 870×	`lower-fma.f32`
4 460×	`lower-*.f64`
4 450×	`lower-*.f32`
3 656×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	467
0	85	453
1	186	453
2	538	453
3	2183	447
4	4467	447
0	8147	429

Stop Event

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

Calls

Call 1

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

localize178.0ms (1.3%)

Memory

-23.5MiB live, 334.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.6%	(/.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	accuracy	98.1%	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (*.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (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	97.3%	(+.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	99.9%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
✓	accuracy	98.2%	(fma.f32 (/.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))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	99.8%	(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
✓	accuracy	99.7%	(*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.9%	(/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.9%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
✓	accuracy	98.2%	(fma.f32 (/.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))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))

Samples

100.0ms

256×

valid

Compiler

Compiled 512 to 53 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-mult: 26.0ms (35.6% of total)

ival-add: 20.0ms (27.4% of total)

ival-div: 17.0ms (23.3% of total)

ival-sqrt: 4.0ms (5.5% of total)

const: 4.0ms (5.5% of total)

ival-pi: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

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

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

series84.0ms (0.6%)

Memory

25.1MiB live, 142.0MiB allocated

Counts

25 → 384

Calls

Call 1

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

Outputs
#<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 (* -6 (* (sqrt (/ (PI) (pow cosTheta 11))) (/ 1 (sqrt -2))))>
#<alt (/ (+ (* -36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))) (* cosTheta (pow (sqrt -2) 2)))) (* -6 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 6))>
#<alt (/ (- (+ (* -6 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2)))) (* -1 (/ (+ (* 36 (/ (* cosTheta (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))))) (pow (sqrt -2) 2))) (* 216 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))) 2) (pow (sqrt -2) 3))))) (pow cosTheta 4)))) (* 36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 6))>
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#<alt (/ 1 (* (pow c 2) cosTheta))>
#<alt (/ (+ (* -1 (/ (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))>
#<alt (/ (- (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (pow cosTheta 2))) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -1 (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))))) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))))) (pow c 3))) (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI)))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))>
#<alt (/ 1 (* (pow c 2) cosTheta))>
#<alt (/ (+ (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (* c cosTheta))) (/ 1 cosTheta)) (pow c 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)))) c)) (+ (* 2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (* c (pow cosTheta 3)))) (/ 1 (* (pow cosTheta 3) (PI))))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))>

Calls

96 calls:

Time	Variable		Point	Expression
17.0ms	c	@	0	(* (/ cosTheta (+ (* (* cosTheta cosTheta) (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ 1 (+ c (/ -1 (sqrt (PI))))))) (neg (/ 1 (PI))))) (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))
10.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
4.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) -1/6) 1/2)) -1)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
4.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) -1/6) 1/2)) -1)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
3.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))

rewrite363.0ms (2.6%)

Memory

18.8MiB live, 439.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 432×	`lower-*.f64`
4 422×	`lower-*.f32`
3 760×	`lower-fma.f64`
3 740×	`lower-fma.f32`
2 978×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	352
0	85	327
1	423	322
2	3986	322
0	8127	311

Stop Event

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

Counts

25 → 751

Calls

Call 1

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

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

simplify492.0ms (3.6%)

Memory

14.5MiB live, 635.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 644×	`lower-*.f64`
6 644×	`lower-*.f32`
5 756×	`lower-fma.f64`
5 756×	`lower-fma.f32`
4 380×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1238	13203
1	4077	12389
0	8142	11738

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 376

Calls

Call 1

Inputs
(* 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)))))))))))
(* -6 (* (sqrt (/ (PI) (pow cosTheta 11))) (/ 1 (sqrt -2))))
(/ (+ (* -36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))) (* cosTheta (pow (sqrt -2) 2)))) (* -6 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 6))
(/ (- (+ (* -6 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2)))) (* -1 (/ (+ (* 36 (/ (* cosTheta (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))))) (pow (sqrt -2) 2))) (* 216 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))) 2) (pow (sqrt -2) 3))))) (pow cosTheta 4)))) (* 36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 6))
(/ (- (+ (* -6 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2)))) (* -1 (/ (+ (* 6 (* (sqrt (* cosTheta (PI))) (/ (* (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))) (+ (* 36 (/ (* cosTheta (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))))) (pow (sqrt -2) 2))) (* 216 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))) 2) (pow (sqrt -2) 3)))))) (sqrt -2)))) (+ (* 36 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (+ (* -1/96 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ 1 (pow (sqrt -2) 5)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))))) (pow (sqrt -2) 2))) (* 216 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))) (pow (sqrt -2) 3)))))) (pow cosTheta 6)))) (+ (* 36 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))))) (* (pow cosTheta 3) (pow (sqrt -2) 2)))) (+ (* 36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))) (* cosTheta (pow (sqrt -2) 2)))) (* 216 (* (sqrt (/ (pow (PI) 3) (pow cosTheta 5))) (/ (pow (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))) 2) (pow (sqrt -2) 3))))))) (pow cosTheta 6))
(* 6 (* (sqrt (/ (PI) (pow cosTheta 11))) (/ (sqrt -1) (sqrt 2))))
(/ (+ (* -36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))) (* cosTheta (pow (sqrt 2) 2)))) (* 6 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 6))
(/ (- (+ (* -1 (/ (+ (* -216 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (sqrt -1) (pow (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) 2)) (pow (sqrt 2) 3)))) (* 36 (/ (* cosTheta (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))))) (pow (sqrt 2) 2)))) (pow cosTheta 4))) (* 6 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (* 36 (/ (* (PI) (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))) (* cosTheta (pow (sqrt 2) 2))))) (pow cosTheta 6))
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(/ 1 c)
(* -1 (/ (- (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
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(* 1/6 (* (sqrt (/ (pow cosTheta 11) (PI))) (* (sqrt -1) (sqrt 2))))
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c
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(/ (+ 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)
(* -1/6 (pow cosTheta 5))
(* (pow cosTheta 5) (- (* 1/2 (/ 1 (pow cosTheta 2))) 1/6))
(* (pow cosTheta 5) (- (* 1/2 (/ 1 (pow cosTheta 2))) (+ 1/6 (/ 1 (pow cosTheta 4)))))
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(* -1 (* (pow cosTheta 5) (- (+ 1/6 (/ 1 (pow cosTheta 4))) (+ (* 1/2 (/ 1 (pow cosTheta 2))) (/ 1 (pow cosTheta 6))))))
1
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(* (pow cosTheta 6) (- (+ (* 1/2 (/ 1 (pow cosTheta 2))) (/ 1 (pow cosTheta 6))) (+ 1/6 (/ 1 (pow cosTheta 4)))))
(* cosTheta (sqrt (PI)))
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(- (/ c cosTheta) (/ 1 cosTheta))
(- (/ c cosTheta) (/ 1 cosTheta))
(- (/ c cosTheta) (/ 1 cosTheta))
(/ c cosTheta)
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(/ c cosTheta)
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(/ (- c 1) cosTheta)
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-1
(- c 1)
(- c 1)
(- c 1)
c
(* c (- 1 (/ 1 c)))
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c
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(* cosTheta (sqrt (PI)))
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(* 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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(* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))
(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (pow cosTheta 4))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 4))
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c
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c
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(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
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1
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(/ 1 c)
(/ (- (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))))) (+ (* -2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))) c)
(/ (- (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (/ 1 (* (pow c 2) (* (pow cosTheta 2) (PI))))))) (+ (* -2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (/ 1 c) (+ (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (- (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) (+ 1 (* -2 (sqrt (/ 1 (PI))))))) (pow c 2)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (pow c 2)))))) c)
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(/ 1 c)
(* -1 (/ (- (* -1 (/ (- (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (+ 1 (+ (* -2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) c)) (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (/ (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) (* c (pow cosTheta 2)))))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (/ (- (+ (* 2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -2 (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (* -1 (/ (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) (pow cosTheta 2))))) c)) (/ (* (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) (- (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* c (pow cosTheta 2)))) (+ (* -2 (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (* -1 (/ (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) (pow cosTheta 2))))) c))))) (* 2 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)) 1) c))
(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))))))
(* -1 (sqrt (PI)))
(+ (* -1 (sqrt (PI))) (* c (sqrt (PI))))
(+ (* -1 (sqrt (PI))) (* c (sqrt (PI))))
(+ (* -1 (sqrt (PI))) (* c (sqrt (PI))))
(* c (sqrt (PI)))
(* c (+ (sqrt (PI)) (* -1 (* (/ 1 c) (sqrt (PI))))))
(* c (+ (sqrt (PI)) (* -1 (* (/ 1 c) (sqrt (PI))))))
(* c (+ (sqrt (PI)) (* -1 (* (/ 1 c) (sqrt (PI))))))
(* c (sqrt (PI)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* (/ 1 c) (sqrt (PI))))))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* (/ 1 c) (sqrt (PI))))))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* (/ 1 c) (sqrt (PI))))))
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
c
(* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))
(* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))
(* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))
(* -1 (* cosTheta (PI)))
(* cosTheta (+ (* -1 (PI)) (* -1 (* (pow cosTheta 2) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))
(* cosTheta (+ (* -1 (PI)) (* (pow cosTheta 2) (- (* -1 (* (pow cosTheta 2) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))
(* cosTheta (+ (* -1 (PI)) (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (* (pow cosTheta 2) (* (pow (PI) 4) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))
(/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))
(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) cosTheta)
(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (+ (/ 1 (* (pow cosTheta 4) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))) cosTheta)
(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (+ (/ 1 (* (pow cosTheta 4) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (+ (/ 1 (* (pow cosTheta 6) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 8)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)
(/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))
(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) cosTheta)
(* -1 (/ (- (* -1 (/ (+ (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (/ 1 (* (pow cosTheta 2) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6))))) (pow cosTheta 2))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) cosTheta))
(* -1 (/ (- (* -1 (/ (+ (/ 1 (* (pow cosTheta 2) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 8)))) (/ 1 (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (pow cosTheta 4))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))) cosTheta))
(/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))))
(+ (* -1 (/ (* c (* (pow cosTheta 3) (+ 2 (* -2 (sqrt (/ 1 (PI))))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))) (/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
(+ (* c (- (* -1 (* c (+ (* -1 (/ (* (pow cosTheta 5) (pow (+ 2 (* -2 (sqrt (/ 1 (PI))))) 2)) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3))) (/ (pow cosTheta 3) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))))) (/ (* (pow cosTheta 3) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2)))) (/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
(+ (* c (- (* c (- (* -1 (* c (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (pow cosTheta 5) (pow (+ 2 (* -2 (sqrt (/ 1 (PI))))) 2)) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3))) (/ (pow cosTheta 3) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))))) (* -1 (/ (* (pow cosTheta 5) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3)))))) (+ (* -1 (/ (* (pow cosTheta 5) (pow (+ 2 (* -2 (sqrt (/ 1 (PI))))) 2)) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3))) (/ (pow cosTheta 3) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))))) (/ (* (pow cosTheta 3) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2)))) (/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
(/ 1 (* (pow c 2) cosTheta))
(/ (+ (* -1 (/ (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/ (- (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (pow cosTheta 2))) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -1 (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))))) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))))) (pow c 3))) (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI)))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/ 1 (* (pow c 2) cosTheta))
(/ (+ (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (* c cosTheta))) (/ 1 cosTheta)) (pow c 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)))) c)) (+ (* 2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (* c (pow cosTheta 3)))) (/ 1 (* (pow cosTheta 3) (PI))))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))

Outputs
(* 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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(* 6 (* (sqrt (/ (PI) (pow cosTheta 11))) (/ (sqrt -1) (sqrt 2))))
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(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (fma.f32 (/.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))) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 c (.f32 c c)))) (-.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 (.f32 (fma.f32 (/.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))) #s(literal 1 binary32)) (fma.f32 (/.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))) #s(literal 1 binary32))) (*.f32 c c)))) c)
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) (* 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 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta c)) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 (/.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))) #s(literal 1 binary32)) (fma.f32 (/.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))) #s(literal 1 binary32))) c) (fma.f32 (/.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))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (/.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))) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (.f32 (fma.f32 (/.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))) #s(literal 1 binary32)) (fma.f32 (/.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))) #s(literal 1 binary32)))) (neg.f32 c)) (fma.f32 (/.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))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (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 (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 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.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))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* -1/6 (* (sqrt (/ (pow cosTheta 11) (PI))) (sqrt -2)))
(.f32 #s(literal -1/6 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 11 binary32)) (PI.f32)))))
(* (pow cosTheta 6) (+ (* -1/6 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/12 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) #s(literal -1/6 binary32) (fma.f32 #s(literal -1/12 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))))))))
(* (pow cosTheta 6) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))) (+ (* -1/6 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/12 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/48 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)))))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) #s(literal -1/6 binary32) (fma.f32 #s(literal -1/12 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 #s(literal 1/48 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32))))))))))
(* (pow cosTheta 6) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/6 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/12 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* -1/96 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/48 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 13) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 6)) (/ c (pow cosTheta 6))))))))))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 11 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) #s(literal -1/6 binary32) (fma.f32 #s(literal -1/12 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (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 9 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 #s(literal -1/96 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 1/48 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 13 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 6 binary32)))))))))))))))
(* 1/6 (* (sqrt (/ (pow cosTheta 11) (PI))) (* (sqrt -1) (sqrt 2))))
(.f32 #s(literal 1/6 binary32) (.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 11 binary32)) (PI.f32)))))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* 1/6 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (-.f32 (.f32 (.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)))) #s(literal 1/6 binary32)) (/.f32 (fma.f32 #s(literal -1/12 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (*.f32 cosTheta cosTheta))))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* 1/6 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (-.f32 (-.f32 (.f32 (.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)))) #s(literal 1/6 binary32)) (/.f32 (fma.f32 #s(literal -1/12 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))) (/.f32 (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 1/48 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/4 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32)))))
(* (pow cosTheta 6) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* 1/48 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* -1/96 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1 (/ (+ (* -1/12 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* 1/6 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 6)) (/ c (pow cosTheta 6))))))))
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(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
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(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(/ 1 cosTheta)
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(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #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)
(* -1/6 (pow cosTheta 5))
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(* (pow cosTheta 5) (- (* 1/2 (/ 1 (pow cosTheta 2))) 1/6))
(.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/6 binary32)))
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(* -1/6 (pow cosTheta 5))
(*.f32 (pow.f32 cosTheta #s(literal 5 binary32)) #s(literal -1/6 binary32))
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(* -1 (* (pow cosTheta 5) (- (+ 1/6 (/ 1 (pow cosTheta 4))) (+ (* 1/2 (/ 1 (pow cosTheta 2))) (/ 1 (pow cosTheta 6))))))
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1
#s(literal 1 binary32)
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(* -1/6 (pow cosTheta 6))
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(* (pow cosTheta 6) (- (* 1/2 (/ 1 (pow cosTheta 2))) 1/6))
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(* -1/6 (pow cosTheta 6))
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(* cosTheta (sqrt (PI)))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ -1 cosTheta)
(/.f32 #s(literal -1 binary32) cosTheta)
(- (/ c cosTheta) (/ 1 cosTheta))
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(- (/ c cosTheta) (/ 1 cosTheta))
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(- (/ c cosTheta) (/ 1 cosTheta))
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ c cosTheta)
(/.f32 c cosTheta)
(* c (- (/ 1 cosTheta) (/ 1 (* c cosTheta))))
(.f32 c (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal -1 binary32) (.f32 cosTheta c))))
(* c (- (/ 1 cosTheta) (/ 1 (* c cosTheta))))
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(* c (- (/ 1 cosTheta) (/ 1 (* c cosTheta))))
(.f32 c (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal -1 binary32) (.f32 cosTheta c))))
(/ c cosTheta)
(/.f32 c cosTheta)
(* -1 (* c (- (/ 1 (* c cosTheta)) (/ 1 cosTheta))))
(.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 #s(literal -1 binary32) cosTheta)) (neg.f32 c))
(* -1 (* c (- (/ 1 (* c cosTheta)) (/ 1 cosTheta))))
(.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 #s(literal -1 binary32) cosTheta)) (neg.f32 c))
(* -1 (* c (- (/ 1 (* c cosTheta)) (/ 1 cosTheta))))
(.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 #s(literal -1 binary32) cosTheta)) (neg.f32 c))
(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
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(/ (- c 1) cosTheta)
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(/ (- c 1) cosTheta)
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(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
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(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
(/ (- c 1) cosTheta)
(/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)
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#s(literal -1 binary32)
(- c 1)
(+.f32 c #s(literal -1 binary32))
(- c 1)
(+.f32 c #s(literal -1 binary32))
(- c 1)
(+.f32 c #s(literal -1 binary32))
c
(* c (- 1 (/ 1 c)))
(*.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) c)))
(* c (- 1 (/ 1 c)))
(*.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) c)))
(* c (- 1 (/ 1 c)))
(*.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) c)))
c
(* -1 (* c (- (/ 1 c) 1)))
(*.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (/ 1 c) 1)))
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(* -1 (* c (- (/ 1 c) 1)))
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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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(* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))
(*.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32)))) (sqrt.f32 #s(literal -2 binary32))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))
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(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (pow cosTheta 4))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 4))
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(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (pow (sqrt -2) 3)))) (+ (* -2 (* (sqrt (* cosTheta (PI))) (/ (* (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (sqrt -2)))) (* 4 (/ (* cosTheta (* (PI) (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))))) (pow (sqrt -2) 2))))) (pow cosTheta 6))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (+ (* -8 (* (sqrt (/ (pow (PI) 3) (pow cosTheta 5))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (+ (* 4 (/ (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))) (* (pow cosTheta 3) (pow (sqrt -2) 2)))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))))) (pow cosTheta 4))
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(* -2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ (sqrt -1) (sqrt 2))))
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(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (* cosTheta (pow (sqrt 2) 2)))) (* -2 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))
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(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 c (.f32 c c)))) (-.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) (*.f32 c c)))) c)
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* 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 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta c)) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (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 (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 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.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))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
(.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 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 5 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32)))))))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 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 5 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (/.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))) #s(literal 1/32 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) #s(literal 1/8 binary32) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 11 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32))))))))))))))
(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32)))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 (.f32 #s(literal -1/2 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))))) (/.f32 (fma.f32 #s(literal 1/4 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 (-.f32 (+.f32 (fma.f32 #s(literal -1/2 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)))) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 #s(literal -1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 #s(literal 1/4 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))) (*.f32 cosTheta cosTheta))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 (-.f32 (-.f32 (+.f32 (fma.f32 #s(literal -1/2 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)))) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) #s(literal 1/32 binary32) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)))) (pow.f32 cosTheta #s(literal 6 binary32)))) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 #s(literal -1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 #s(literal 1/4 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))))
(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) 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 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) c))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
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(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
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(fma.f32 c (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (.f32 c (*.f32 cosTheta cosTheta))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))))
(- (+ (* c (+ (* c (pow cosTheta 2)) (* (pow cosTheta 2) (+ 2 (* -2 (sqrt (/ 1 (PI)))))))) (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (/ 1 (PI)))
(fma.f32 c (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (.f32 c (*.f32 cosTheta cosTheta))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))))
(* (pow c 2) (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) (*.f32 c c))
(* (pow c 2) (+ (/ (* (pow cosTheta 2) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) c) (pow cosTheta 2)))
(.f32 (.f32 c c) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) c) (.f32 cosTheta cosTheta)))
(* (pow c 2) (- (+ (/ (* (pow cosTheta 2) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) c) (+ (/ (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (pow c 2)) (pow cosTheta 2))) (/ 1 (* (pow c 2) (PI)))))
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(* (pow c 2) (- (+ (/ (* (pow cosTheta 2) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) c) (+ (/ (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (pow c 2)) (pow cosTheta 2))) (/ 1 (* (pow c 2) (PI)))))
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(* (pow c 2) (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) (*.f32 c c))
(* (pow c 2) (+ (* 2 (/ (* (pow cosTheta 2) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)) (pow cosTheta 2)))
(.f32 (.f32 c c) (fma.f32 #s(literal 2 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (*.f32 cosTheta cosTheta)))
(* (pow c 2) (+ (* -1 (/ (+ (* -2 (* (pow cosTheta 2) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (/ (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) c))) c)) (pow cosTheta 2)))
(.f32 (.f32 c c) (fma.f32 cosTheta cosTheta (/.f32 (fma.f32 (.f32 #s(literal -2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (neg.f32 c))) (neg.f32 c))))
(* (pow c 2) (+ (* -1 (/ (+ (* -2 (* (pow cosTheta 2) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* -1 (/ (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) c))) c)) (pow cosTheta 2)))
(.f32 (.f32 c c) (fma.f32 cosTheta cosTheta (/.f32 (fma.f32 (.f32 #s(literal -2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (neg.f32 c))) (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 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)) (sqrt (pow (PI) 3)))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (neg.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))))))
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(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))
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(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))))
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(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.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))) (.f32 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))))))))
(+ (* -1 (/ (- (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (/ 1 (* cosTheta (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (+.f32 (/.f32 (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)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.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)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))) cosTheta))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) cosTheta)) (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (-.f32 (/.f32 (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)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.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)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (*.f32 cosTheta (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) cosTheta)) cosTheta))
(/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))))
(*.f32 cosTheta (/.f32 (-.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32)))))
(+ (* c (- (/ (pow cosTheta 2) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (/ (* (pow cosTheta 3) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2)))) (/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
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(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) cosTheta)
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(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (+ (/ 1 (* (pow cosTheta 4) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))) cosTheta)
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(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (+ (/ 1 (* (pow cosTheta 4) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (+ (/ 1 (* (pow cosTheta 6) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 8)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)
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(/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))
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(/ (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) cosTheta)
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(* -1 (/ (- (* -1 (/ (+ (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (/ 1 (* (pow cosTheta 2) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6))))) (pow cosTheta 2))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) cosTheta))
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(* -1 (/ (- (* -1 (/ (+ (/ 1 (* (pow cosTheta 2) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 8)))) (/ 1 (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 6)))) (pow cosTheta 4))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))) cosTheta))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 8 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 6 binary32))))) (neg.f32 (pow.f32 cosTheta #s(literal 4 binary32)))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32)))))) (neg.f32 cosTheta))
(/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))))
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(+ (* -1 (/ (* c (* (pow cosTheta 3) (+ 2 (* -2 (sqrt (/ 1 (PI))))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))) (/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
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(+ (* c (- (* -1 (* c (+ (* -1 (/ (* (pow cosTheta 5) (pow (+ 2 (* -2 (sqrt (/ 1 (PI))))) 2)) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3))) (/ (pow cosTheta 3) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))))) (/ (* (pow cosTheta 3) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2)))) (/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
(fma.f32 c (neg.f32 (fma.f32 c (fma.f32 (neg.f32 (pow.f32 cosTheta #s(literal 5 binary32))) (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (pow.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(literal 3 binary32))) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32)))))) (/.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))))))) (/.f32 cosTheta (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32)))))
(+ (* c (- (* c (- (* -1 (* c (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (pow cosTheta 5) (pow (+ 2 (* -2 (sqrt (/ 1 (PI))))) 2)) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3))) (/ (pow cosTheta 3) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))))) (* -1 (/ (* (pow cosTheta 5) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3)))))) (+ (* -1 (/ (* (pow cosTheta 5) (pow (+ 2 (* -2 (sqrt (/ 1 (PI))))) 2)) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 3))) (/ (pow cosTheta 3) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2))))) (/ (* (pow cosTheta 3) (+ 2 (* -2 (sqrt (/ 1 (PI)))))) (pow (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))) 2)))) (/ cosTheta (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))))
(fma.f32 c (fma.f32 c (neg.f32 (fma.f32 c (neg.f32 (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (fma.f32 (neg.f32 (pow.f32 cosTheta #s(literal 5 binary32))) (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (pow.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(literal 3 binary32))) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))))))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32)))) (/.f32 (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (pow.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(literal 3 binary32))))) (fma.f32 (neg.f32 (pow.f32 cosTheta #s(literal 5 binary32))) (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (pow.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) #s(literal 3 binary32))) (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32)))))))) (neg.f32 (/.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (*.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))))))) (/.f32 cosTheta (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32)))))
(/ 1 (* (pow c 2) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c c)))
(/ (+ (* -1 (/ (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) c)) (*.f32 c c))
(/ (- (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (+.f32 (fma.f32 (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) (.f32 c c)) (/.f32 #s(literal 2 binary32) (.f32 cosTheta c))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (.f32 c c)))))) (.f32 c c))
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (pow cosTheta 2))) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -1 (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))))) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))))) (pow c 3))) (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI)))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/.f32 (-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))) (.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (.f32 cosTheta (neg.f32 cosTheta))))) (.f32 c (.f32 c c)))) (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (+.f32 (fma.f32 (neg.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -2 binary32) #s(literal 2 binary32))) (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) (.f32 c c)) (/.f32 #s(literal 2 binary32) (.f32 cosTheta c))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (.f32 c c)))))) (.f32 c c))
(/ 1 (* (pow c 2) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c c)))
(/ (+ (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (* c cosTheta))) (/ 1 cosTheta)) (pow c 2))
(/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 c c))
(/ (+ (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 #s(literal 3 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))) (neg.f32 c)) (.f32 #s(literal 2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) c)) (*.f32 c c))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)))) c)) (+ (* 2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (* c (pow cosTheta 3)))) (/ 1 (* (pow cosTheta 3) (PI))))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (+.f32 (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 #s(literal 3 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))) c) (+.f32 (fma.f32 #s(literal 2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) cosTheta) (/.f32 #s(literal -1 binary32) (PI.f32))) (.f32 c (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 #s(literal 3 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))) (neg.f32 c)) (.f32 #s(literal 2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) c)) (*.f32 c c))

eval325.0ms (2.4%)

Memory: -10.8MiB live, 463.8MiB allocated
Compiler: Compiled 78 630 to 6 254 computations (92% saved)

prune608.0ms (4.4%)

Memory

-174.6MiB live, 649.0MiB allocated

Pruning

40 alts after pruning (38 fresh and 2 done)

	Pruned	Kept	Total
New	1 836	29	1 865
Fresh	12	9	21
Picked	4	1	5
Done	0	1	1
Total	1 852	40	1 892

Accuracy

100.0%

Counts

1 892 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.5%	(pow.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal -1/2 binary32))
	92.1%	(/.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c))))
	92.8%	(/.f32 (*.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) c)) (/.f32 (-.f32 #s(literal 1 binary32) c) cosTheta))
▶	95.1%	(/.f32 cosTheta (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)))))
▶	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (*.f32 (/.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)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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))) #s(literal 1 binary32)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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) (/.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) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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 (fma.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
▶	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
	97.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 (.f32 cosTheta (*.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c))) (+.f32 #s(literal 1 binary32) c))))
	92.3%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) c))) (neg.f32 c))))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) c))) (sqrt.f32 (PI.f32)))))
	85.8%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) c) (*.f32 (+.f32 #s(literal -1 binary32) c) cosTheta)) (sqrt.f32 (PI.f32))))
	85.8%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) (*.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	92.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) c) (.f32 cosTheta (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
✓	5.0%	(/.f32 #s(literal 1 binary32) c)
	96.4%	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (*.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (+.f32 cosTheta (fma.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
	96.3%	(*.f32 (/.f32 cosTheta (/.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)))))
	92.7%	(.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c)))
	96.0%	(*.f32 (/.f32 #s(literal 1 binary32) (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)
	53.0%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 (.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)))) (.f32 cosTheta cosTheta)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))))
	92.8%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) c)) (.f32 cosTheta (*.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c))))
	92.7%	(*.f32 (+.f32 #s(literal -1 binary32) c) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (+.f32 #s(literal -1 binary32) c) cosTheta)))
▶	92.7%	(.f32 (.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) c))
	96.1%	(.f32 (.f32 (PI.f32) (neg.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)))))
	92.6%	(*.f32 (sqrt.f32 (PI.f32)) (/.f32 (+.f32 #s(literal -1 binary32) c) (/.f32 (+.f32 #s(literal -1 binary32) c) cosTheta)))
	96.0%	(*.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))))
	92.0%	(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
▶	90.9%	(.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
✓	92.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 787 to 1 053 computations (41.1% saved)

simplify514.0ms (3.7%)

Memory

-4.6MiB live, 893.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f32 (/.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)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	160	(*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	160	(/.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)
✓	cost-diff	0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	0	(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	0	(/.f32 cosTheta (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)))))
✓	cost-diff	672	(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))))
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(sqrt.f32 (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
✓	cost-diff	1120	(*.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(+.f32 #s(literal -1 binary32) c)
✓	cost-diff	0	(/.f32 cosTheta (+.f32 #s(literal -1 binary32) c))
✓	cost-diff	0	(*.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32)))
✓	cost-diff	704	(.f32 (.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) c))
✓	cost-diff	0	(.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)))
✓	cost-diff	0	(fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	160	(fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))

Rules

17 392×	`lower-fma.f64`
17 378×	`lower-fma.f32`
4 044×	`lower-*.f64`
4 030×	`lower-*.f32`
3 028×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	334
0	75	324
1	139	324
2	292	316
3	656	298
4	1596	298
5	4183	291
0	8605	284

Stop Event

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

Calls

Call 1

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

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

localize266.0ms (1.9%)

Memory

1.4MiB live, 273.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.2%	(fma.f32 (/.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)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.5%	(sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	99.7%	(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))))
✓	accuracy	98.2%	(/.f32 cosTheta (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)))))
✓	accuracy	96.9%	(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.8%	(.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
✓	accuracy	96.9%	(sqrt.f32 (sqrt.f32 (PI.f32)))
✓	accuracy	95.0%	(*.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32))))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.8%	(/.f32 cosTheta (+.f32 #s(literal -1 binary32) c))
✓	accuracy	99.7%	(.f32 (.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) c))
✓	accuracy	98.6%	(*.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32)))
✓	accuracy	99.9%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))

Samples

107.0ms

256×

valid

Compiler

Compiled 370 to 46 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-mult: 53.0ms (60.7% of total)

ival-div: 13.0ms (14.9% of total)

ival-add: 10.0ms (11.5% of total)

ival-sqrt: 8.0ms (9.2% of total)

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

ival-sub: 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)

series22.0ms (0.2%)

Memory

17.5MiB live, 55.0MiB allocated

Counts

25 → 312

Calls

Call 1

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

Outputs
#<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 (* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))>
#<alt (* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))>
#<alt (* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))>
#<alt (* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))>
#<alt (* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))>
#<alt (* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))>
#<alt (* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))>
#<alt (* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))>
#<alt (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))>
#<alt (+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))>
#<alt c>
#<alt (* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))>
#<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 (* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))>
#<alt (/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))>
#<alt (/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (pow cosTheta 4))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 4))>
#<alt (/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (pow (sqrt -2) 3)))) (+ (* -2 (* (sqrt (* cosTheta (PI))) (/ (* (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (sqrt -2)))) (* 4 (/ (* cosTheta (* (PI) (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))))) (pow (sqrt -2) 2))))) (pow cosTheta 6))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (+ (* -8 (* (sqrt (/ (pow (PI) 3) (pow cosTheta 5))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (+ (* 4 (/ (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))) (* (pow cosTheta 3) (pow (sqrt -2) 2)))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))))) (pow cosTheta 4))>
#<alt (* -2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ (sqrt -1) (sqrt 2))))>
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#<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))))))))>

Calls

78 calls:

Time	Variable		Point	Expression
3.0ms	c	@	inf	(/ cosTheta (+ -1 c))
1.0ms	cosTheta	@	inf	(/ cosTheta (+ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))
1.0ms	cosTheta	@	0	(* (/ cosTheta (+ -1 c)) (sqrt (PI)))
1.0ms	cosTheta	@	-inf	(/ cosTheta (+ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))
0.0ms	cosTheta	@	inf	(* (/ cosTheta (+ -1 c)) (sqrt (PI)))

rewrite617.0ms (4.5%)

Memory

-11.4MiB live, 894.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 826×	`lower-*.f64`
5 812×	`lower-*.f32`
4 000×	`lower-fma.f64`
3 986×	`lower-fma.f32`
3 000×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	261
0	75	243
1	326	237
2	2268	237
0	8365	230

Stop Event

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

Counts

25 → 1 975

Calls

Call 1

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

Outputs
(exp.f32 (neg.f32 (.f32 (log1p.f32 (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)))) #s(literal -1 binary32))))
(+.f32 #s(literal 1 binary32) (+.f32 c (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta))))
(+.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) 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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)))
(+.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (+.f32 #s(literal 1 binary32) c))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) c)
(+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32))
(pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta))))) (fma.f32 (/.f32 (.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 cosTheta (.f32 cosTheta cosTheta))) (.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)))) (.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 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (fma.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (neg.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))) #s(literal -1 binary32))
(fma.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) c))
(fma.f32 c #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))
(fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (fma.f32 cosTheta (.f32 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))
(fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (fma.f32 c (.f32 c c) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)))
(fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)))
(fma.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
(-.f32 (/.f32 (.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c)))) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta))))) (fma.f32 (/.f32 (.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 cosTheta (.f32 cosTheta cosTheta))) (.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (fma.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (neg.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))))
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(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal 2 binary32)))
(.f32 (sqrt.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (sqrt.f32 (sqrt.f32 (sqrt.f32 (PI.f32)))) #s(literal 4 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 (sqrt.f32 (PI.f32)))) #s(literal 4 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (cbrt.f32 (PI.f32))) #s(literal 3 binary32)))
(.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32)) (cbrt.f32 (PI.f32)))
(.f32 (pow.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (pow.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32))) #s(literal 1/3 binary32)) (pow.f32 (*.f32 (PI.f32) (sqrt.f32 (PI.f32))) #s(literal 1/3 binary32)))
(.f32 (pow.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) #s(literal 1/3 binary32)) (cbrt.f32 (sqrt.f32 (PI.f32))))
(.f32 (pow.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/3 binary32)) (cbrt.f32 (cbrt.f32 (PI.f32))))
(.f32 (exp.f32 (.f32 #s(literal 2 binary32) (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))))) (exp.f32 (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32)))))
(.f32 (cbrt.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (cbrt.f32 (*.f32 (PI.f32) (sqrt.f32 (PI.f32)))))
(.f32 (cbrt.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32)))) (cbrt.f32 (sqrt.f32 (PI.f32))))
(.f32 (cbrt.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (cbrt.f32 (cbrt.f32 (PI.f32))))
(.f32 (sqrt.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (PI.f32))))) (cbrt.f32 (PI.f32)))
(.f32 (sqrt.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(log.f32 (exp.f32 (PI.f32)))
(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 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (*.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))) #s(literal 1/4 binary32))
(pow.f32 (exp.f32 (log.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))) #s(literal 1/2 binary32))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal 1 binary32))))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32))) (sqrt.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32))) (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)))))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (neg.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))))
(/.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 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) #s(literal 1 binary32))) (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (PI.f32))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))) (sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)) (PI.f32))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) #s(literal -1 binary32))) (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (neg.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) #s(literal -1 binary32))) (sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)) (neg.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (.f32 #s(literal -1 binary32) (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)))) (sqrt.f32 (.f32 (neg.f32 (PI.f32)) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))))
(/.f32 (sqrt.f32 (.f32 #s(literal -1 binary32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)))) (sqrt.f32 (*.f32 (neg.f32 (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)))))
(/.f32 (sqrt.f32 (.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)))) (sqrt.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))))
(/.f32 (sqrt.f32 (.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)))))
(/.f32 (sqrt.f32 (neg.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))) (sqrt.f32 (neg.f32 (neg.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal -1 binary32))) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)))) (sqrt.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(*.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))
(*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32)))))
(*.f32 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)) (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(*.f32 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32))))

simplify495.0ms (3.6%)

Memory

45.3MiB live, 782.1MiB allocated

Algorithm

1×	egg-herbie

Rules

8 636×	`lower-fma.f64`
8 636×	`lower-fma.f32`
6 820×	`lower-*.f64`
6 820×	`lower-*.f32`
3 856×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	660	9504
1	2099	8910
2	7922	8895
0	8184	8390

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 306

Calls

Call 1

Inputs
(* (/ 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)
(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))
(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))
(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* 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)))))))))))
(* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))
(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (pow cosTheta 4))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 4))
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(* -2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ (sqrt -1) (sqrt 2))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (* cosTheta (pow (sqrt 2) 2)))) (* -2 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))
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(/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
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(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* (/ 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)
(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))
(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))
(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (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 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 (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))) (* -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))))))))

Outputs
(* (/ 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 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ 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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(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
(.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 1/2 binary32)))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
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(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))
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(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))
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(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
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(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
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(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))
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c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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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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(* 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 (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 (+.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))) (.f32 #s(literal -3/2 binary32) (PI.f32)))) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(/.f32 (+.f32 #s(literal -1 binary32) (/.f32 (-.f32 (/.f32 (fma.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32)) (neg.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32))) (/.f32 (pow.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32)) #s(literal 3 binary32)) c)) (neg.f32 c)) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32))) (neg.f32 c))) (neg.f32 c))
1
#s(literal 1 binary32)
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(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))
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(* 1/2 (pow cosTheta 4))
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(* cosTheta (- (* 1/2 (pow cosTheta 2)) 1))
(.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)))
(* 1/2 (pow cosTheta 3))
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(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* 1/2 (pow cosTheta 3))
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(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (neg.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
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(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (neg.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
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(/ (+ (* cosTheta (sqrt (PI))) (+ (* (/ cosTheta c) (sqrt (PI))) (* (/ cosTheta (pow c 2)) (sqrt (PI))))) c)
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (/.f32 cosTheta (.f32 c c)) (+.f32 cosTheta (/.f32 cosTheta c)))) c)
(/ (+ (* cosTheta (sqrt (PI))) (+ (* (/ cosTheta c) (sqrt (PI))) (+ (* (/ cosTheta (pow c 2)) (sqrt (PI))) (* (/ cosTheta (pow c 3)) (sqrt (PI)))))) c)
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (+.f32 cosTheta (/.f32 cosTheta c)) (+.f32 (/.f32 cosTheta (.f32 c c)) (/.f32 cosTheta (.f32 c (.f32 c c)))))) c)
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(/.f32 (*.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (/.f32 cosTheta c))) c)
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(* -1 (/ (+ (* -1 (* cosTheta (sqrt (PI)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* cosTheta (sqrt (PI)))) (* -1 (* (/ cosTheta c) (sqrt (PI))))) c)) (* cosTheta (sqrt (PI)))) c))) c))
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(/ cosTheta (- c 1))
(/.f32 cosTheta (+.f32 c #s(literal -1 binary32)))
(/ cosTheta (- c 1))
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(/ cosTheta (- c 1))
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(/ cosTheta (- c 1))
(/.f32 cosTheta (+.f32 c #s(literal -1 binary32)))
(/ cosTheta (- c 1))
(/.f32 cosTheta (+.f32 c #s(literal -1 binary32)))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* -1 (* c cosTheta)))
(neg.f32 (fma.f32 cosTheta c cosTheta))
(+ (* -1 cosTheta) (* c (- (* -1 (* c cosTheta)) cosTheta)))
(fma.f32 (neg.f32 c) (fma.f32 cosTheta c cosTheta) (neg.f32 cosTheta))
(+ (* -1 cosTheta) (* c (- (* c (- (* -1 (* c cosTheta)) cosTheta)) cosTheta)))
(fma.f32 c (fma.f32 (neg.f32 c) (fma.f32 cosTheta c cosTheta) (neg.f32 cosTheta)) (neg.f32 cosTheta))
(/ cosTheta c)
(/.f32 cosTheta c)
(/ (+ cosTheta (/ cosTheta c)) c)
(/.f32 (+.f32 cosTheta (/.f32 cosTheta c)) c)
(/ (- (+ cosTheta (/ cosTheta (pow c 2))) (* -1 (/ cosTheta c))) c)
(/.f32 (+.f32 (/.f32 cosTheta (*.f32 c c)) (+.f32 cosTheta (/.f32 cosTheta c))) c)
(/ (- (+ cosTheta (/ cosTheta (pow c 3))) (+ (* -1 (/ cosTheta c)) (* -1 (/ cosTheta (pow c 2))))) c)
(/.f32 (+.f32 cosTheta (+.f32 (/.f32 cosTheta (.f32 c (.f32 c c))) (/.f32 (+.f32 cosTheta (/.f32 cosTheta c)) c))) c)
(/ cosTheta c)
(/.f32 cosTheta c)
(* -1 (/ (+ (* -1 cosTheta) (* -1 (/ cosTheta c))) c))
(/.f32 (+.f32 cosTheta (/.f32 cosTheta c)) c)
(* -1 (/ (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (/ cosTheta c)) c))) c))
(/.f32 (-.f32 (neg.f32 cosTheta) (/.f32 (+.f32 cosTheta (/.f32 cosTheta c)) c)) (neg.f32 c))
(* -1 (/ (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* -1 (/ (+ (* -1 cosTheta) (* -1 (/ cosTheta c))) c))) c))) c))
(/.f32 (-.f32 (/.f32 (-.f32 (neg.f32 cosTheta) (/.f32 (+.f32 cosTheta (/.f32 cosTheta c)) c)) c) cosTheta) (neg.f32 c))
-1
#s(literal -1 binary32)
(- c 1)
(+.f32 c #s(literal -1 binary32))
(- c 1)
(+.f32 c #s(literal -1 binary32))
(- c 1)
(+.f32 c #s(literal -1 binary32))
c
(* c (- 1 (/ 1 c)))
(+.f32 c (*.f32 c (/.f32 #s(literal -1 binary32) c)))
(* c (- 1 (/ 1 c)))
(+.f32 c (*.f32 c (/.f32 #s(literal -1 binary32) c)))
(* c (- 1 (/ 1 c)))
(+.f32 c (*.f32 c (/.f32 #s(literal -1 binary32) c)))
c
(* -1 (* c (- (/ 1 c) 1)))
(neg.f32 (fma.f32 c (/.f32 #s(literal 1 binary32) c) (neg.f32 c)))
(* -1 (* c (- (/ 1 c) 1)))
(neg.f32 (fma.f32 c (/.f32 #s(literal 1 binary32) c) (neg.f32 c)))
(* -1 (* c (- (/ 1 c) 1)))
(neg.f32 (fma.f32 c (/.f32 #s(literal 1 binary32) c) (neg.f32 c)))
(* cosTheta (sqrt (PI)))
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(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
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(*.f32 cosTheta (sqrt.f32 (PI.f32)))
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(* cosTheta (sqrt (PI)))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(sqrt (/ 1 (PI)))
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(+ (sqrt (/ 1 (PI))) (* cosTheta (- 1 (sqrt (/ 1 (PI))))))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 (neg.f32 (.f32 cosTheta (PI.f32))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2)) (sqrt (pow (PI) 3))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
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(/ 1 (- 1 (sqrt (/ 1 (PI)))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (- 1 (sqrt (/ 1 (PI))))))
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(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (/ 1 (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI)))))
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(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (- 1 (sqrt (/ 1 (PI)))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (/ 1 (- 1 (sqrt (/ 1 (PI))))))) (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI)))))
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(/ 1 (- 1 (sqrt (/ 1 (PI)))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (- 1 (sqrt (/ 1 (PI))))))
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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)
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(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
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(* 1/2 (pow cosTheta 3))
(.f32 cosTheta (.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32))))
(* (pow cosTheta 3) (- 1/2 (/ 1 (pow cosTheta 2))))
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(* 1/2 (pow cosTheta 3))
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(/ 1 (PI))
(/.f32 #s(literal 1 binary32) (PI.f32))
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(fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
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(* -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)))))
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(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
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(* -2 (/ cosTheta (PI)))
(/.f32 (*.f32 cosTheta #s(literal -2 binary32)) (PI.f32))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
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(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
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(* 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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(* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))
(*.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32)))) (sqrt.f32 #s(literal -2 binary32))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))
(/.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (.f32 (PI.f32) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))))) cosTheta) (/.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 cosTheta #s(literal 4 binary32)))
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(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/16 binary32)) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32))))))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/16 binary32)) (fma.f32 #s(literal 1/32 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 (/.f32 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) #s(literal 1/8 binary32)) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 11 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32)))))))))))))
(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
(.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))) (.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 binary32)))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32)))) (sqrt.f32 #s(literal 2 binary32)) (/.f32 (fma.f32 #s(literal 1/4 binary32) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (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)))))) (*.f32 cosTheta (neg.f32 cosTheta)))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 (-.f32 (fma.f32 #s(literal -1/2 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)))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 #s(literal -1/16 binary32) (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 #s(literal 1/4 binary32) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (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)))))) (*.f32 cosTheta cosTheta))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))
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(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))
c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) c)
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(neg.f32 (fma.f32 c (/.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32)) (neg.f32 c)) (neg.f32 c)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(neg.f32 (fma.f32 c (/.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32)) (neg.f32 c)) (neg.f32 c)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -1/2 binary32) #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -1/2 binary32) #s(literal -1/2 binary32)))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(.f32 cosTheta (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.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 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/8 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 1/16 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 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.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 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/8 binary32)))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (sqrt.f32 #s(literal 2 binary32)) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (neg.f32 cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/2 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)))))))
(.f32 (neg.f32 cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal -1/8 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/2 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))))))))
(neg.f32 (.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal -1/8 binary32)) (fma.f32 (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)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/2 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) (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 cosTheta #s(literal -1/2 binary32) #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta 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 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))))
(+ (* 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 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32))))))
(+ (* -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 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.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 #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 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.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 #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)))) (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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 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 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (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 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 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 (PI))
(/.f32 #s(literal 1 binary32) (PI.f32))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (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))))))
(.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)))))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -1/2 binary32) #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -1/2 binary32) #s(literal -1/2 binary32)))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(.f32 cosTheta (fma.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))))))
(* 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 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.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 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/8 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 1/16 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 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.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 #s(literal -1/2 binary32) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/8 binary32)))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (sqrt.f32 #s(literal 2 binary32)) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (neg.f32 cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/2 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)))))))
(.f32 (neg.f32 cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal -1/8 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/2 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))))))))
(neg.f32 (.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal -1/8 binary32)) (fma.f32 (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)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/2 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)))))))))

eval352.0ms (2.6%)

Memory: 13.2MiB live, 958.2MiB allocated
Compiler: Compiled 135 679 to 7 352 computations (94.6% saved)

prune402.0ms (2.9%)

Memory

6.2MiB live, 808.3MiB allocated

Pruning

43 alts after pruning (38 fresh and 5 done)

	Pruned	Kept	Total
New	2 708	19	2 727
Fresh	14	19	33
Picked	2	3	5
Done	0	2	2
Total	2 724	43	2 767

Accuracy

100.0%

Counts

2 767 → 43

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.5%	(pow.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal -1/2 binary32))
	92.8%	(/.f32 (*.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) c)) (/.f32 (-.f32 #s(literal 1 binary32) c) cosTheta))
	92.8%	(/.f32 (.f32 cosTheta (.f32 (+.f32 #s(literal -1 binary32) c) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal -1 binary32) c))
✓	95.1%	(/.f32 cosTheta (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)))))
	98.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
	98.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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))) #s(literal 1 binary32)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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 (fma.f32 cosTheta (/.f32 #s(literal -2 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
✓	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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))) #s(literal 1 binary32)))
	97.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.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)))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
	95.7%	(/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 (.f32 cosTheta (*.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c))) (+.f32 #s(literal 1 binary32) c))))
	92.3%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) c))) (neg.f32 c))))
	85.8%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 c #s(literal -1 binary32)) cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
	92.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) c) (.f32 cosTheta (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
✓	5.0%	(/.f32 #s(literal 1 binary32) c)
	96.4%	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (*.f32 (+.f32 #s(literal 1 binary32) (+.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)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (+.f32 cosTheta (fma.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
	53.2%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta)) (neg.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.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 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))))
	95.9%	(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)
	90.1%	(.f32 (.f32 (fma.f32 (neg.f32 c) (fma.f32 cosTheta c cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) c))
	92.7%	(.f32 (.f32 (/.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 c c))) (-.f32 #s(literal -1 binary32) c)) (+.f32 #s(literal -1 binary32) c))
	92.6%	(.f32 (.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32))) (+.f32 c (*.f32 c (/.f32 #s(literal -1 binary32) c))))
✓	92.7%	(.f32 (.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) c))
	86.0%	(.f32 (.f32 (/.f32 cosTheta (+.f32 #s(literal -1 binary32) c)) (sqrt.f32 (PI.f32))) #s(literal -1 binary32))
	89.0%	(.f32 (.f32 (sqrt.f32 (PI.f32)) (neg.f32 (fma.f32 cosTheta c cosTheta))) (+.f32 #s(literal -1 binary32) c))
	86.0%	(.f32 (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) c))
	96.1%	(.f32 (.f32 (PI.f32) (neg.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)))))
	92.8%	(.f32 (.f32 cosTheta (/.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) c))) (+.f32 #s(literal -1 binary32) c))
	92.6%	(*.f32 (sqrt.f32 (PI.f32)) (/.f32 (+.f32 #s(literal -1 binary32) c) (/.f32 (+.f32 #s(literal -1 binary32) c) cosTheta)))
	96.0%	(*.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))))
	95.8%	(.f32 cosTheta (fma.f32 (neg.f32 (.f32 cosTheta (PI.f32))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
	92.0%	(*.f32 cosTheta (fma.f32 (neg.f32 cosTheta) (fma.f32 (PI.f32) (+.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))))
	92.8%	(.f32 cosTheta (.f32 (sqrt.f32 (sqrt.f32 (*.f32 (PI.f32) (sqrt.f32 (PI.f32))))) (sqrt.f32 (sqrt.f32 (sqrt.f32 (PI.f32))))))
✓	92.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 3 120 to 974 computations (68.8% saved)

regimes163.0ms (1.2%)

Memory

-19.9MiB live, 263.5MiB allocated

Counts

92 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

29.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
28.0ms	(/.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)))))
26.0ms	(.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	c
25.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.5%	1	`cosTheta`
98.5%	1	`c`
98.5%	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)))))`
98.5%	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))))`
98.5%	1	`(+.f32 #s(literal 1 binary32) c)`
98.5%	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)

regimes95.0ms (0.7%)

Memory

-15.0MiB live, 182.7MiB allocated

Counts

55 → 1

Calls

Call 1

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

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

Calls

6 calls:

17.0ms	(+.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))))
16.0ms	c
16.0ms	(/.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)))
14.0ms	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes114.0ms (0.8%)

Memory

22.0MiB live, 103.7MiB allocated

Counts

51 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

32.0ms	(+.f32 #s(literal 1 binary32) c)
25.0ms	c
14.0ms	(+.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))))
14.0ms	(.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)))
14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.0%	1	`cosTheta`
98.0%	1	`c`
98.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.0%	1	`(+.f32 #s(literal 1 binary32) c)`
98.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes89.0ms (0.6%)

Memory

-6.1MiB live, 117.1MiB allocated

Counts

47 → 1

Calls

Call 1

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

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (/.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:

21.0ms	c
15.0ms	(.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))))
13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
13.0ms	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)

regimes85.0ms (0.6%)

Memory

0.6MiB live, 157.1MiB allocated

Counts

46 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

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)

regimes77.0ms (0.6%)

Memory

11.7MiB live, 168.5MiB allocated

Counts

44 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
97.5%	1	`c`
97.5%	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)))))`
97.5%	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))))`
97.5%	1	`(+.f32 #s(literal 1 binary32) c)`
97.5%	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

-7.3MiB live, 150.9MiB allocated

Counts

37 → 1

Calls

Call 1

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

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (/.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:

12.0ms	cosTheta
12.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
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))))
10.0ms	c
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
97.4%	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 (.f32 (/.f32 #s(literal 1 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)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes64.0ms (0.5%)

Memory

10.7MiB live, 123.7MiB allocated

Counts

36 → 1

Calls

Call 1

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

Outputs

(*.f32 (*.f32 (PI.f32) (neg.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)))))

Calls

6 calls:

11.0ms	c
11.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
11.0ms	(+.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	(/.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)))))
10.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.1%	1	`cosTheta`
96.1%	1	`c`
96.1%	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)))))`
96.1%	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))))`
96.1%	1	`(+.f32 #s(literal 1 binary32) c)`
96.1%	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)

regimes106.0ms (0.8%)

Memory

-31.3MiB live, 146.5MiB allocated

Counts

35 → 1

Calls

Call 1

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

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

Calls

6 calls:

51.0ms	(.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	c
11.0ms	cosTheta
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes47.0ms (0.3%)

Memory

17.5MiB live, 100.8MiB allocated

Counts

24 → 1

Calls

Call 1

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

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

Calls

6 calls:

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)))
8.0ms	c
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)))))
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.8%	1	`cosTheta`
95.8%	1	`c`
95.8%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
95.8%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes45.0ms (0.3%)

Memory

-9.7MiB live, 108.6MiB allocated

Counts

22 → 1

Calls

Call 1

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

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

Calls

6 calls:

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	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 (.f32 (/.f32 #s(literal 1 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	c

Results

Accuracy	Segments	Branch
92.8%	1	`cosTheta`
92.8%	1	`c`
92.8%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
92.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
92.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
92.8%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes9.0ms (0.1%)

Memory

-10.0MiB live, 29.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	(+.f32 (+.f32 #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 #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	`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 #s(literal 1 binary32) c)`
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	`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)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

simplify10.0ms (0.1%)

Memory

28.6MiB live, 28.6MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary32`
22×	`+-commutative_binary32`
16×	`sub-neg_binary32`
14×	`neg-sub0_binary32`
14×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	228
1	89	228
2	105	228
3	118	228
4	124	228
5	127	228
6	128	228

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (9.8%)

Memory

-13.8MiB live, 1 272.1MiB allocated

Rules

9 656×	`lower-fma.f64`
9 656×	`lower-fma.f32`
8 636×	`lower-fma.f64`
8 636×	`lower-fma.f32`
7 286×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	317
0	86	300
1	361	285
2	3098	234
0	9127	234
0	1238	13203
1	4077	12389
0	8142	11738
0	1418	15236
1	4803	14772
0	8939	14075
0	660	9504
1	2099	8910
2	7922	8895
0	8184	8390
0	41	352
0	85	327
1	423	322
2	3986	322
0	8127	311
0	37	261
0	75	243
1	326	237
2	2268	237
0	8365	230
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311

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

Compiler

Compiled 577 to 288 computations (50.1% saved)

preprocess97.0ms (0.7%)

Memory: -5.2MiB live, 112.0MiB allocated
Compiler: Compiled 514 to 162 computations (68.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze37.0ms (0.3%)

sample2.2s (16.3%)

preprocess241.0ms (1.8%)

explain322.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify203.0ms (1.5%)

localize139.0ms (1%)

series32.0ms (0.2%)

rewrite432.0ms (3.1%)

simplify473.0ms (3.4%)

eval73.0ms (0.5%)

prune140.0ms (1%)

simplify368.0ms (2.7%)

localize218.0ms (1.6%)

series92.0ms (0.7%)

rewrite256.0ms (1.9%)

simplify537.0ms (3.9%)

eval186.0ms (1.4%)

prune210.0ms (1.5%)

simplify426.0ms (3.1%)

localize178.0ms (1.3%)

series84.0ms (0.6%)

rewrite363.0ms (2.6%)

simplify492.0ms (3.6%)

eval325.0ms (2.4%)

prune608.0ms (4.4%)

simplify514.0ms (3.7%)

localize266.0ms (1.9%)

series22.0ms (0.2%)

rewrite617.0ms (4.5%)

simplify495.0ms (3.6%)

eval352.0ms (2.6%)

prune402.0ms (2.9%)

regimes163.0ms (1.2%)

regimes95.0ms (0.7%)

regimes114.0ms (0.8%)

regimes89.0ms (0.6%)

regimes85.0ms (0.6%)

regimes77.0ms (0.6%)

regimes67.0ms (0.5%)

regimes64.0ms (0.5%)

regimes106.0ms (0.8%)

regimes47.0ms (0.3%)

regimes45.0ms (0.3%)

regimes9.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.3s (9.8%)

preprocess97.0ms (0.7%)

end0.0ms (0%)

Profiling