Metrics for Beckmann Sample, normalization factor

analyze49.0ms (0.2%)

Memory

2.1MiB live, 40.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.2s (10.7%)

Memory

-29.2MiB live, 3 246.0MiB allocated

Samples

1.7s	8 256×	0	valid
18.0ms	75×	0	invalid

Precisions

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

ival-mult: 467.0ms (33% of total)

ival-div: 186.0ms (13.1% of total)

const: 155.0ms (11% of total)

ival-sqrt: 112.0ms (7.9% of total)

ival-sub: 92.0ms (6.5% of total)

ival-<: 92.0ms (6.5% of total)

ival-add: 87.0ms (6.1% of total)

ival-exp: 79.0ms (5.6% of total)

ival-pi: 72.0ms (5.1% of total)

ival-neg: 34.0ms (2.4% of total)

ival-and: 23.0ms (1.6% of total)

exact: 14.0ms (1% of total)

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

Bogosity

preprocess252.0ms (1.3%)

Memory

-32.5MiB live, 181.9MiB 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)))))

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)))

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)))

explain329.0ms (1.6%)

Memory

-8.9MiB live, 388.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

60.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 9.0ms (21.1% of total)

ival-mult: 8.0ms (18.8% of total)

ival-sqrt: 7.0ms (16.4% of total)

ival-add: 5.0ms (11.7% of total)

ival-exp: 4.0ms (9.4% of total)

ival-sub: 4.0ms (9.4% of total)

ival-pi: 2.0ms (4.7% of total)

ival-neg: 2.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

97.5%

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

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize54.0ms (0.3%)

Memory

27.9MiB live, 103.9MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

30.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

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

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

ival-mult: 4.0ms (18.8% of total)

ival-add: 3.0ms (14.1% of total)

ival-sqrt: 3.0ms (14.1% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.1%)

Memory

-16.1MiB live, 27.5MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))>
#<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 #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) 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 (+ 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>
#<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

12 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta	@	-inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
5.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
4.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
2.0ms	cosTheta	@	inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
1.0ms	c	@	0	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))

rewrite302.0ms (1.5%)

Memory

8.2MiB live, 392.7MiB 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	47
0	33	47
1	141	42
2	1060	39
0	8551	39

Stop Event

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

Counts

4 → 223

Calls

Call 1

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

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

simplify398.0ms (2%)

Memory

41.3MiB live, 627.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 852×	`lower-fma.f64`
9 852×	`lower-fma.f32`
5 796×	`lower-*.f64`
5 796×	`lower-*.f32`
3 472×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	337	2435
1	1029	2348
2	4041	2233
0	8861	2122

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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

eval41.0ms (0.2%)

Memory: -1.5MiB live, 111.5MiB allocated
Compiler: Compiled 11 511 to 1 832 computations (84.1% saved)

prune64.0ms (0.3%)

Memory

-60.9MiB live, 133.6MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	256	15	271
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	256	16	272

Accuracy

99.9%

Counts

272 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	92.4%	(pow.f32 (pow.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	49.3%	(/.f32 (+.f32 #s(literal 1 binary32) (-.f32 c (/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) cosTheta))) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (neg.f32 (.f32 cosTheta cosTheta)))))))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.4%	(/.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 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (.f32 cosTheta (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	4.9%	(/.f32 #s(literal 1 binary32) c)
▶	97.5%	(.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))))
▶	98.0%	(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (neg.f32 (-.f32 (.f32 (.f32 (PI.f32) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (fma.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32)))) (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))) (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))))
	96.4%	(*.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) (sqrt.f32 (PI.f32))))
	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	85.2%	(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) c)) #s(literal -1 binary32)))

Compiler

Compiled 1 037 to 552 computations (46.8% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize303.0ms (1.5%)

Memory

20.9MiB live, 690.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.3%	(PI.f32)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (.f32 cosTheta (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.2%	(.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (*.f32 cosTheta (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))) cosTheta))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	97.3%	(fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))
✓	accuracy	96.9%	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.3%	(PI.f32)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.0%	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	96.9%	(.f32 (.f32 (PI.f32) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32)))
✓	accuracy	96.9%	(*.f32 (PI.f32) (PI.f32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))

Samples

119.0ms	254×	0	valid
4.0ms	2×	5	exit

Compiler

Compiled 1 616 to 76 computations (95.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 96.0ms

ival-mult: 45.0ms (46.9% of total)

ival-div: 15.0ms (15.6% of total)

ival-add: 14.0ms (14.6% of total)

ival-sqrt: 7.0ms (7.3% of total)

ival-neg: 5.0ms (5.2% of total)

ival-sub: 4.0ms (4.2% of total)

ival-exp: 2.0ms (2.1% of total)

adjust: 1.0ms (1% of total)

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

exact: 1.0ms (1% of total)

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

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

series23.0ms (0.1%)

Memory

25.6MiB live, 60.9MiB allocated

Counts

13 → 108

Calls

Call 1

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

Outputs
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#<alt (/ 1 c)>
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#<alt (/ 1 c)>
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Calls

27 calls:

Time	Variable		Point	Expression
6.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (/ (sqrt (/ 1 (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))))
4.0ms	c	@	0	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ (+ (* (neg (* cosTheta cosTheta)) (/ 1 (- 1 cosTheta))) cosTheta) (* cosTheta (/ 1 (- 1 cosTheta))))) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
1.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (* (/ (sqrt (/ 1 (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))))
1.0ms	cosTheta	@	0	(/ (sqrt (/ 1 (PI))) cosTheta)
1.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ (+ (* (neg (* cosTheta cosTheta)) (/ 1 (- 1 cosTheta))) cosTheta) (* cosTheta (/ 1 (- 1 cosTheta))))) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))

rewrite376.0ms (1.9%)

Memory

-35.1MiB live, 532.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 586×	`lower-*.f64`
5 564×	`lower-*.f32`
4 234×	`lower-fma.f64`
4 230×	`lower-fma.f32`
3 372×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	138
0	77	132
1	300	115
2	2354	109
0	8786	108

Stop Event

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

Counts

13 → 460

Calls

Call 1

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

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

simplify390.0ms (1.9%)

Memory

15.0MiB live, 555.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 124×	`lower-fma.f64`
7 124×	`lower-fma.f32`
6 530×	`lower-*.f64`
6 530×	`lower-*.f32`
2 372×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	496	3839
1	1567	3663
2	5975	3591
0	8402	3474

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 106

Calls

Call 1

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

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

eval8.0s (39.9%)

Memory: 20.5MiB live, 1 844.2MiB allocated
Compiler: Compiled 395 110 to 24 711 computations (93.7% saved)

prune2.0s (9.8%)

Memory

-16.8MiB live, 2 722.3MiB allocated

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	3 933	17	3 950
Fresh	7	3	10
Picked	3	2	5
Done	0	1	1
Total	3 943	23	3 966

Accuracy

100.0%

Counts

3 966 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.7%	(pow.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (PI.f32))) cosTheta) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
▶	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	92.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) #s(literal 1 binary32)))
	45.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (.f32 cosTheta (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))) #s(literal 1 binary32)))
▶	93.5%	(/.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))))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.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) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	93.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 (E.f32))))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	97.4%	(/.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 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (PI.f32))) cosTheta) c)))
▶	10.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
✓	4.9%	(/.f32 #s(literal 1 binary32) c)
	29.6%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (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))))
	49.8%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (.f32 cosTheta (neg.f32 cosTheta))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	97.4%	(.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 (*.f32 (PI.f32) (log.f32 (E.f32))))))
	97.4%	(.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 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))))) (sqrt.f32 (PI.f32))))
	94.0%	(*.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 c (PI.f32) (PI.f32))) (sqrt.f32 (PI.f32))))
	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 250 to 700 computations (44% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize240.0ms (1.2%)

Memory

11.6MiB live, 521.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.3%	(PI.f32)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.2%	(.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))) cosTheta))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	99.3%	(PI.f32)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
✓	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))) #s(literal 1 binary32))
✓	accuracy	97.4%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	99.3%	(PI.f32)
✓	accuracy	99.2%	(/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	99.0%	(/.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))))))
✓	accuracy	99.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	100.0%	(+.f32 #s(literal 1 binary32) c)
✓	accuracy	99.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.2%	(/.f32 (sqrt.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	99.1%	(*.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
✓	accuracy	99.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))

Samples

121.0ms	254×	0	valid
5.0ms	2×	5	exit

Compiler

Compiled 554 to 51 computations (90.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-div: 55.0ms (54.2% of total)

ival-mult: 17.0ms (16.7% of total)

ival-add: 10.0ms (9.8% of total)

ival-sqrt: 7.0ms (6.9% of total)

ival-sub: 5.0ms (4.9% of total)

ival-exp: 4.0ms (3.9% of total)

adjust: 1.0ms (1% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.1%)

Memory

37.0MiB live, 76.0MiB allocated

Counts

15 → 192

Calls

Call 1

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

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

Calls

48 calls:

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

rewrite303.0ms (1.5%)

Memory

-9.0MiB live, 623.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 186×	`lower-/.f64`
4 158×	`lower-/.f32`
3 648×	`lower-*.f64`
3 632×	`lower-*.f32`
2 708×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	207
0	90	191
1	381	186
2	3185	182
0	9211	180

Stop Event

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

Counts

15 → 470

Calls

Call 1

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

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

simplify473.0ms (2.3%)

Memory

-16.3MiB live, 720.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 382×	`lower-fma.f64`
9 382×	`lower-fma.f32`
7 826×	`lower-*.f64`
7 826×	`lower-*.f32`
4 114×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	792	8764
1	2518	8442
0	8079	8176

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 190

Calls

Call 1

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

eval108.0ms (0.5%)

Memory: 3.4MiB live, 231.8MiB allocated
Compiler: Compiled 33 411 to 3 681 computations (89% saved)

prune134.0ms (0.7%)

Memory

0.7MiB live, 317.6MiB allocated

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	922	22	944
Fresh	11	4	15
Picked	4	1	5
Done	3	0	3
Total	940	27	967

Accuracy

100.0%

Counts

967 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 1 binary32)))
	41.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (-.f32 cosTheta (/.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32))))))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) #s(literal 1 binary32)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) 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))
	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal 1/2 binary32) 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))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))
▶	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	93.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32))))))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)))))
▶	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	72.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	72.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (PI.f32))) (/.f32 (sqrt.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	93.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
✓	10.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	10.5%	(-.f32 #s(literal 1 binary32) c)
	29.6%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (exp.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) #s(literal 3 binary32))) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (sqrt.f32 (PI.f32))))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (/.f32 (-.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)) (.f32 (.f32 cosTheta (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 cosTheta cosTheta))))))
	49.8%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32))))) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (.f32 cosTheta (neg.f32 cosTheta))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
▶	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	97.4%	(.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 (*.f32 (PI.f32) (log.f32 (E.f32))))))
	94.0%	(*.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 (PI.f32) c (PI.f32))) (sqrt.f32 (PI.f32))))
	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
▶	10.4%	#s(literal 1 binary32)

Compiler

Compiled 1 283 to 761 computations (40.7% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize161.0ms (0.8%)

Memory

11.4MiB live, 331.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 1 binary32)))
✓	accuracy	98.2%	(fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (fma.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 1 binary32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))
✓	accuracy	100.0%	(/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.8%	(/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))
✓	accuracy	99.7%	(fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))
✓	accuracy	98.9%	(*.f32 cosTheta (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
✓	accuracy	96.9%	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (PI.f32)) (PI.f32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.2%	(sqrt.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (PI.f32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.9%	(*.f32 (/.f32 (sqrt.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (PI.f32))))
✓	accuracy	98.7%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (PI.f32))

Samples

91.0ms

256×

valid

Compiler

Compiled 446 to 53 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 21.0ms (31.6% of total)

ival-div: 16.0ms (24.1% of total)

ival-add: 11.0ms (16.6% of total)

ival-exp: 6.0ms (9% of total)

ival-sqrt: 6.0ms (9% of total)

ival-neg: 3.0ms (4.5% of total)

ival-pi: 2.0ms (3% 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)

series44.0ms (0.2%)

Memory

-0.2MiB live, 80.0MiB allocated

Counts

15 → 192

Calls

Call 1

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

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

Calls

48 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ (sqrt (+ (* (neg cosTheta) (/ cosTheta (- 1 cosTheta))) cosTheta)) cosTheta) (sqrt (/ (+ (/ 1 cosTheta) -1) (PI)))) (exp (* (neg cosTheta) cosTheta)))))
4.0ms	c	@	0	(/ 1 (+ (+ 1 c) (* (* (/ (sqrt (+ (* (neg cosTheta) (/ cosTheta (- 1 cosTheta))) cosTheta)) cosTheta) (sqrt (/ (+ (/ 1 cosTheta) -1) (PI)))) (exp (* (neg cosTheta) cosTheta)))))
2.0ms	cosTheta	@	0	(+ (+ 1 c) (/ (/ (exp (neg (* cosTheta cosTheta))) cosTheta) (sqrt (PI))))
2.0ms	cosTheta	@	-inf	(* (/ (sqrt (+ (* (neg cosTheta) (/ cosTheta (- 1 cosTheta))) cosTheta)) cosTheta) (sqrt (/ (+ (/ 1 cosTheta) -1) (PI))))
2.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (+ (* cosTheta (* (sqrt (/ 1 (PI))) (+ (* -1/2 cosTheta) -1))) (sqrt (/ 1 (PI))))) 1))

rewrite372.0ms (1.8%)

Memory

-15.7MiB live, 460.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 862×	`lower-fma.f64`
3 850×	`lower-fma.f32`
3 714×	`lower-*.f64`
3 700×	`lower-*.f32`
3 594×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	221
0	91	221
1	379	202
2	3138	196
0	9017	196

Stop Event

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

Counts

15 → 614

Calls

Call 1

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

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

simplify458.0ms (2.3%)

Memory

46.8MiB live, 434.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 814×	`lower-fma.f64`
9 814×	`lower-fma.f32`
7 930×	`lower-*.f64`
7 930×	`lower-*.f32`
4 028×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	786	6375
1	2556	5825
0	8302	5633

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 190

Calls

Call 1

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

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

eval169.0ms (0.8%)

Memory: 0.5MiB live, 161.7MiB allocated
Compiler: Compiled 28 687 to 3 490 computations (87.8% saved)

prune199.0ms (1%)

Memory

-22.2MiB live, 331.5MiB allocated

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	866	10	876
Fresh	11	10	21
Picked	4	1	5
Done	0	1	1
Total	881	22	903

Accuracy

100.0%

Counts

903 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.4%	(fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 (.f32 cosTheta cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))
	96.4%	(fma.f32 (sqrt.f32 (PI.f32)) cosTheta (neg.f32 (.f32 (.f32 cosTheta (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta)))
	96.6%	(/.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) (*.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (neg.f32 (PI.f32))) cosTheta) (fma.f32 (neg.f32 cosTheta) (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 (sqrt.f32 (PI.f32)))))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) 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))
	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal 1/2 binary32) 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))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) 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))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) #s(literal 1 binary32)))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
✓	10.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	10.5%	(-.f32 #s(literal 1 binary32) c)
	96.4%	(*.f32 (fma.f32 (neg.f32 cosTheta) (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) cosTheta)
	56.8%	(.f32 (.f32 cosTheta cosTheta) (+.f32 (neg.f32 (PI.f32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	96.4%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	94.0%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) c (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	96.3%	(.f32 cosTheta (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32) (neg.f32 (.f32 cosTheta (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))))))
	94.9%	(.f32 cosTheta (.f32 (fma.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (PI.f32)) (neg.f32 cosTheta)))
	94.1%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	10.4%	#s(literal 1 binary32)

Compiler

Compiled 1 998 to 598 computations (70.1% saved)

regimes150.0ms (0.7%)

Memory

-6.3MiB live, 150.7MiB allocated

Counts

65 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

35.0ms	(+.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))))
35.0ms	(.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
17.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
17.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.1%	1	`cosTheta`
98.1%	1	`c`
98.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.1%	1	`(+.f32 #s(literal 1 binary32) c)`
98.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes116.0ms (0.6%)

Memory

16.5MiB live, 134.2MiB allocated

Counts

47 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

26.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
26.0ms	c
24.0ms	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	(.f32 (.f32 (/.f32 #s(literal 1 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
97.8%	1	`cosTheta`
97.8%	1	`c`
97.8%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.8%	1	`(+.f32 #s(literal 1 binary32) c)`
97.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 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)

regimes130.0ms (0.6%)

Memory

-3.5MiB live, 117.7MiB allocated

Counts

35 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

48.0ms	c
30.0ms	cosTheta
20.0ms	(+.f32 #s(literal 1 binary32) 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)))
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes134.0ms (0.7%)

Memory

-1.1MiB live, 120.4MiB allocated

Counts

33 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

41.0ms	c
39.0ms	(.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	cosTheta
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes104.0ms (0.5%)

Memory

3.0MiB live, 118.6MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs

(*.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 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))))) (sqrt.f32 (PI.f32))))

Calls

6 calls:

27.0ms	cosTheta
25.0ms	c
22.0ms	(+.f32 #s(literal 1 binary32) c)
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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)))))

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes104.0ms (0.5%)

Memory

17.7MiB live, 101.9MiB allocated

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

36.0ms	(/.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)))))
33.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	c
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	cosTheta

Results

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

regimes58.0ms (0.3%)

Memory

-4.6MiB live, 121.1MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

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)))
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
7.0ms	c
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.7%	1	`cosTheta`
96.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.7%	1	`c`
96.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.7%	1	`(+.f32 #s(literal 1 binary32) c)`
96.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes48.0ms (0.2%)

Memory

-21.7MiB live, 96.7MiB allocated

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

11.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
8.0ms	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	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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
96.7%	1	`cosTheta`
96.7%	1	`c`
96.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.7%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes45.0ms (0.2%)

Memory

10.3MiB live, 128.5MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs

(/.f32 (*.f32 (fma.f32 (*.f32 cosTheta cosTheta) (*.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (neg.f32 (PI.f32))) cosTheta) (fma.f32 (neg.f32 cosTheta) (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 (sqrt.f32 (PI.f32)))))

Calls

6 calls:

8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
8.0ms	c
8.0ms	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	(/.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
96.6%	1	`cosTheta`
96.6%	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)))))`
96.6%	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))))`
96.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.6%	1	`c`
96.6%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes44.0ms (0.2%)

Memory

-10.3MiB live, 109.4MiB allocated

Counts

21 → 1

Calls

Call 1

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

Outputs
(fma.f32 (sqrt.f32 (PI.f32)) cosTheta (neg.f32 (.f32 (.f32 cosTheta (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta)))

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)))))
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	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))))
6.0ms	c

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes23.0ms (0.1%)

Memory

20.3MiB live, 58.9MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
(*.f32 (fma.f32 (neg.f32 cosTheta) (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) cosTheta)

Calls

6 calls:

5.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	c
3.0ms	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes39.0ms (0.2%)

Memory

-24.9MiB live, 55.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

21.0ms	c
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
3.0ms	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes26.0ms (0.1%)

Memory

1.0MiB live, 40.2MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

6 calls:

15.0ms	cosTheta
2.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
2.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
2.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	c

Results

Accuracy	Segments	Branch
10.5%	1	`cosTheta`
10.5%	1	`c`
10.5%	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)))))`
10.5%	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))))`
10.5%	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)))`
10.5%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes9.0ms (0%)

Memory

30.0MiB live, 30.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)

Outputs
#s(literal 1 binary32)

Calls

6 calls:

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	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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
10.4%	1	`(+.f32 #s(literal 1 binary32) c)`
10.4%	1	`cosTheta`
10.4%	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)))))`
10.4%	1	`c`
10.4%	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))))`
10.4%	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)

simplify74.0ms (0.4%)

Memory

-24.7MiB live, 96.0MiB allocated

Algorithm

1×	egg-herbie

Rules

572×	`distribute-lft-neg-in_binary32`
524×	`unsub-neg_binary32`
406×	`neg-mul-1_binary32`
308×	`cancel-sign-sub_binary32`
294×	`neg-sub0_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	277
1	145	277
2	181	277
3	207	275
4	236	275
5	259	275
6	365	275
7	583	275
8	745	275
9	905	275
10	1171	275
11	1471	275
12	1820	275
13	1992	275
14	2047	275
15	2053	275
16	2053	275

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (7.5%)

Memory

11.5MiB live, 1 494.1MiB allocated

Rules

9 852×	`lower-fma.f64`
9 852×	`lower-fma.f32`
9 814×	`lower-fma.f64`
9 814×	`lower-fma.f32`
9 382×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	337	2435
1	1029	2348
2	4041	2233
0	8861	2122
0	40	138
0	77	132
1	300	115
2	2354	109
0	8786	108
0	45	221
0	91	221
1	379	202
2	3138	196
0	9017	196
0	792	8764
1	2518	8442
0	8079	8176
0	18	47
0	33	47
1	141	42
2	1060	39
0	8551	39
0	45	207
0	90	191
1	381	186
2	3185	182
0	9211	180
0	786	6375
1	2556	5825
0	8302	5633
0	496	3839
1	1567	3663
2	5975	3591
0	8402	3474

Stop Event

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

Compiler

Compiled 465 to 221 computations (52.5% saved)

preprocess71.0ms (0.4%)

Memory: -5.8MiB live, 149.5MiB allocated
Compiler: Compiled 608 to 216 computations (64.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze49.0ms (0.2%)

sample2.2s (10.7%)

preprocess252.0ms (1.3%)

explain329.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify0.0ms (0%)

localize54.0ms (0.3%)

series24.0ms (0.1%)

rewrite302.0ms (1.5%)

simplify398.0ms (2%)

eval41.0ms (0.2%)

prune64.0ms (0.3%)

simplify0.0ms (0%)

localize303.0ms (1.5%)

series23.0ms (0.1%)

rewrite376.0ms (1.9%)

simplify390.0ms (1.9%)

eval8.0s (39.9%)

prune2.0s (9.8%)

simplify0.0ms (0%)

localize240.0ms (1.2%)

series27.0ms (0.1%)

rewrite303.0ms (1.5%)

simplify473.0ms (2.3%)

eval108.0ms (0.5%)

prune134.0ms (0.7%)

simplify0.0ms (0%)

localize161.0ms (0.8%)

series44.0ms (0.2%)

rewrite372.0ms (1.8%)

simplify458.0ms (2.3%)

eval169.0ms (0.8%)

prune199.0ms (1%)

regimes150.0ms (0.7%)

regimes116.0ms (0.6%)

regimes130.0ms (0.6%)

regimes134.0ms (0.7%)

regimes104.0ms (0.5%)

regimes104.0ms (0.5%)

regimes58.0ms (0.3%)

regimes48.0ms (0.2%)

regimes45.0ms (0.2%)

regimes44.0ms (0.2%)

regimes23.0ms (0.1%)

regimes39.0ms (0.2%)

regimes26.0ms (0.1%)

regimes9.0ms (0%)

simplify74.0ms (0.4%)

soundness1.5s (7.5%)

preprocess71.0ms (0.4%)

end0.0ms (0%)

Profiling