Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze26.0ms (0.3%)

Memory

18.7MiB live, 18.7MiB 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 (22.9%)

Memory

2.1MiB live, 2 831.0MiB allocated

Samples

1.5s	8 256×	0	valid
9.0ms	67×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-mult: 224.0ms (17.1% of total)

ival-div: 200.0ms (15.2% of total)

ival-sqrt: 179.0ms (13.6% of total)

const: 147.0ms (11.2% of total)

ival-sub: 121.0ms (9.2% of total)

ival-add: 107.0ms (8.1% of total)

ival-neg: 100.0ms (7.6% of total)

ival-<: 87.0ms (6.6% of total)

ival-exp: 77.0ms (5.9% of total)

ival-pi: 31.0ms (2.4% of total)

ival-and: 22.0ms (1.7% of total)

exact: 15.0ms (1.1% of total)

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

Bogosity

explain446.0ms (4.6%)

Memory

12.8MiB live, 560.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
2	-	2	(6.385801179836051e-40 -1.8194712985050154e-33)	`(/.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	-	1	(2.3528403774353338e-39 5.471359764607305e-38)	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`
0	-	0	-	`(sqrt.f32 (PI.f32))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(*.f32 (neg.f32 cosTheta) cosTheta)`
0	-	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	-	0	-	`(+.f32 #s(literal 1 binary32) c)`
0	-	0	-	`cosTheta`
0	-	0	-	`(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))`
0	-	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	-	0	-	`c`
0	-	0	-	`(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))`
0	-	0	-	`(-.f32 #s(literal 1 binary32) cosTheta)`
0	-	0	-	`(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)`
0	-	0	-	`#s(literal 1 binary32)`
0	-	0	-	`(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)`
0	-	0	-	`(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))`
0	-	0	-	`(neg.f32 cosTheta)`

Confusion

	Predicted +	Predicted -
+	0	3
-	0	253

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	3
-	0	0	253

Precision?

0/0

Recall?

0.0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0.0

Samples

100.0ms

512×

valid

Compiler

Compiled 533 to 156 computations (70.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-sqrt: 26.0ms (31.8% of total)

ival-neg: 17.0ms (20.8% of total)

ival-div: 10.0ms (12.2% of total)

ival-add: 9.0ms (11% of total)

ival-mult: 9.0ms (11% of total)

ival-sub: 5.0ms (6.1% of total)

ival-exp: 4.0ms (4.9% of total)

ival-pi: 2.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess209.0ms (2.2%)

Memory

13.1MiB live, 104.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Compiler

Compiled 25 to 18 computations (28% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.2%	(/.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

▶

97.2%

(/.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 25 to 18 computations (28% saved)

simplify139.0ms (1.4%)

Memory

1.8MiB live, 40.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize160.0ms (1.7%)

Memory

-3.7MiB live, 71.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.12175751953688403	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.4088220337643558	(/.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	0.6731839036024426	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
accuracy	1.0	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))

Samples

148.0ms

256×

valid

Compiler

Compiled 254 to 38 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-div: 114.0ms (84% of total)

ival-sqrt: 8.0ms (5.9% of total)

ival-mult: 4.0ms (2.9% of total)

ival-add: 3.0ms (2.2% of total)

ival-exp: 2.0ms (1.5% of total)

ival-sub: 2.0ms (1.5% of total)

ival-pi: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series39.0ms (0.4%)

Memory

4.2MiB live, 47.7MiB allocated

Counts

6 → 58

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
22.0ms	cosTheta	@	inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (sqrt (PI))) (- (- 1 cosTheta) cosTheta))
8.0ms	cosTheta	@	-inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (sqrt (PI))) (- (- 1 cosTheta) cosTheta))
2.0ms	cosTheta	@	0	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (sqrt (PI))) (- (- 1 cosTheta) cosTheta))
2.0ms	c	@	0	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (sqrt (PI))) (- (- 1 cosTheta) cosTheta))
1.0ms	c	@	inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (sqrt (PI))) (- (- 1 cosTheta) cosTheta))

simplify164.0ms (1.7%)

Memory

0.2MiB live, 262.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	407	3010
1	1237	2916
2	4721	2838
0	8274	2706

Stop Event

1×	iter limit
1×	node limit

Counts

58 → 57

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

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

rewrite189.0ms (2%)

Memory

0.4MiB live, 206.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	73
0	33	73
1	141	66
2	1060	61
0	8551	61

Stop Event

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

Counts

6 → 456

Calls

Call 1

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

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

eval86.0ms (0.9%)

Memory: 21.4MiB live, 127.7MiB allocated
Compiler: Compiled 21 227 to 2 805 computations (86.8% saved)

prune31.0ms (0.3%)

Memory

-21.9MiB live, 62.3MiB allocated

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	486	23	509
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	487	23	510

Accuracy

99.8%

Counts

510 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.2%	(/.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))))
	14.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
▶	13.3%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	89.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))))) (*.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)))
	14.3%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 #s(literal 1 binary32) c) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	97.7%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	97.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) cosTheta)))
	48.5%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	69.6%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.5%	(/.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)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	94.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.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)))))
	90.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	90.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	32.7%	(-.f32 (/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (/.f32 (*.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))))
	56.1%	(*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)))
▶	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	91.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))

Compiler

Compiled 1 536 to 924 computations (39.8% saved)

simplify177.0ms (1.8%)

Memory

28.8MiB live, 213.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	96	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (*.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
cost-diff	192	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))
cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
cost-diff	512	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
cost-diff	0	(+.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	352	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
cost-diff	544	(/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32)))
cost-diff	0	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.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)))))
cost-diff	192	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.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))))
cost-diff	0	(/.f32 #s(literal 1 binary32) c)
cost-diff	0	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
cost-diff	0	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	629
0	102	606
1	160	596
2	309	587
3	711	572
4	1428	568
5	3571	568
0	8107	539

Stop Event

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

Calls

Call 1

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

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

localize178.0ms (1.8%)

Memory

0.1MiB live, 285.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
accuracy	0.48140758522334853	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
accuracy	25.896296065936088	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (*.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
accuracy	30.139645962152375	(fma.f32 c c #s(literal -1 binary32))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (.f32 (.f32 (/.f32 #s(literal 1 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	0.6731839036024426	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
accuracy	1.0	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
accuracy	26.753887150442527	(fma.f32 c c #s(literal -1 binary32))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.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)))))
accuracy	0.54296875	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	1.1855763817563592	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
accuracy	0	(/.f32 #s(literal 1 binary32) c)
accuracy	30.398648446357203	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy	0.12175751953688403	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.2265625	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3515625	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Samples

133.0ms

256×

valid

Compiler

Compiled 1 223 to 107 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-pow: 36.0ms (32.8% of total)

ival-div: 21.0ms (19.1% of total)

ival-add: 19.0ms (17.3% of total)

ival-mult: 19.0ms (17.3% of total)

ival-sqrt: 5.0ms (4.6% of total)

ival-exp: 4.0ms (3.6% of total)

ival-sub: 3.0ms (2.7% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series102.0ms (1.1%)

Memory

-7.4MiB live, 114.7MiB allocated

Counts

23 → 157

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
40.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (+ (* c c) -1) (- c 1)) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI)))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* cosTheta (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (+ (* c c) -1) (/ 1 (sqrt (PI))))
18.0ms	cosTheta	@	inf	((/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (+ (* c c) -1) (- c 1)) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI)))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* cosTheta (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (+ (* c c) -1) (/ 1 (sqrt (PI))))
16.0ms	c	@	0	((/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (+ (* c c) -1) (- c 1)) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI)))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* cosTheta (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (+ (* c c) -1) (/ 1 (sqrt (PI))))
10.0ms	cosTheta	@	0	((/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (+ (* c c) -1) (- c 1)) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI)))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* cosTheta (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (+ (* c c) -1) (/ 1 (sqrt (PI))))
5.0ms	c	@	inf	((/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (+ (* c c) -1) (- c 1)) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (/ (+ (* c c) -1) (- c 1)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI)))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* cosTheta (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (+ (* c c) -1) (/ 1 (sqrt (PI))))

simplify215.0ms (2.2%)

Memory

7.0MiB live, 197.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1113	11146
1	3566	10624
0	8328	10101

Stop Event

1×	iter limit
1×	node limit

Counts

157 → 156

Calls

Call 1

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

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

rewrite165.0ms (1.7%)

Memory

22.2MiB live, 247.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	395
0	102	374
1	384	349
2	3048	344
0	8102	337

Stop Event

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

Counts

23 → 943

Calls

Call 1

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

Outputs
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))
(*.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)))
(*.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (exp.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))) #s(literal -1 binary32))
(pow.f32 (*.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))) #s(literal -1/2 binary32))
(pow.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))) #s(literal -1 binary32))
(pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))))
(.f32 (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)))))
(*.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal 1 binary32))
(/.f32 (neg.f32 (-.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)))) (neg.f32 (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32)))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 2 binary32)))) (neg.f32 (-.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))))
(/.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 3 binary32)))) (neg.f32 (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 2 binary32)) (*.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32))))) (neg.f32 (neg.f32 (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32))))) (neg.f32 (neg.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))))
(/.f32 (neg.f32 (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c))))) (neg.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
(/.f32 (neg.f32 (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32))))) (neg.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (-.f32 #s(literal 1 binary32) c) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))) (neg.f32 (.f32 (-.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(/.f32 (neg.f32 (fma.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))) (neg.f32 (.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(/.f32 (-.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 2 binary32))) (-.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 2 binary32)) (*.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)))))
(/.f32 (neg.f32 (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (neg.f32 (.f32 #s(literal 1 binary32) (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))))
(/.f32 (neg.f32 (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))))
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(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(pow.f32 (/.f32 (/.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal -1 binary32))
(exp.f32 (*.f32 (log.f32 (/.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))) #s(literal -1 binary32)))
(neg.f32 (/.f32 (neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta))
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(expm1.f32 (*.f32 (log.f32 c) #s(literal 2 binary32)))
(*.f32 (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 c c #s(literal 1 binary32))))
(.f32 (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (*.f32 c c) #s(literal -1 binary32)))))
(*.f32 (-.f32 c #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)))
(*.f32 (+.f32 c #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32)))
(/.f32 (neg.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 c #s(literal 1 binary32)))) (neg.f32 (-.f32 #s(literal 1 binary32) c)))
(/.f32 (neg.f32 (*.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32)))) (neg.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (neg.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (neg.f32 (fma.f32 c c (+.f32 c #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (neg.f32 (*.f32 (-.f32 #s(literal 1 binary32) c) (fma.f32 c c (+.f32 c #s(literal 1 binary32))))))
(/.f32 (neg.f32 (.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 c c #s(literal -1 binary32)))) (neg.f32 (.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (neg.f32 (.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (fma.f32 c c (+.f32 c #s(literal 1 binary32))))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 c #s(literal 4 binary32)))) (neg.f32 (-.f32 #s(literal -1 binary32) (*.f32 c c))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)))) (neg.f32 (neg.f32 (fma.f32 c c #s(literal 1 binary32)))))
(/.f32 (neg.f32 (neg.f32 (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32))))))
(/.f32 (neg.f32 (-.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal 1 binary32))) (neg.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 c c)))))
(/.f32 (neg.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (fma.f32 c c #s(literal -1 binary32)))) (neg.f32 (+.f32 c #s(literal 1 binary32))))
(/.f32 (neg.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (fma.f32 c c #s(literal -1 binary32)))) (neg.f32 (*.f32 (-.f32 #s(literal 1 binary32) c) (+.f32 c #s(literal 1 binary32)))))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 c #s(literal 1 binary32))) (-.f32 #s(literal 1 binary32) c))
(/.f32 (*.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32))) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32))) (fma.f32 c c (+.f32 c #s(literal 1 binary32))))
(/.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (+.f32 c #s(literal 1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 c #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 c c)))
(/.f32 (-.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 c #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 c c))))
(/.f32 (neg.f32 (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32))) (neg.f32 (fma.f32 c c #s(literal 1 binary32))))
(/.f32 (neg.f32 (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32))) (neg.f32 (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 c #s(literal 4 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32))))))
(/.f32 (neg.f32 (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32))) (neg.f32 (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32)))))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (fma.f32 c c #s(literal -1 binary32))) (*.f32 (-.f32 #s(literal 1 binary32) c) (+.f32 c #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32))) (*.f32 (-.f32 #s(literal 1 binary32) c) (fma.f32 c c (+.f32 c #s(literal 1 binary32)))))
(/.f32 (.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 c c #s(literal -1 binary32))) (.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
(/.f32 (.f32 (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (fma.f32 c c (+.f32 c #s(literal 1 binary32)))))
(/.f32 (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 c c #s(literal 1 binary32)))
(/.f32 (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 c #s(literal 4 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32)))))
(/.f32 (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32)) (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (fma.f32 c c #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32))) (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 c c #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32))) (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 c c))) (/.f32 (pow.f32 c #s(literal 4 binary32)) (-.f32 #s(literal -1 binary32) (.f32 c c))))
(-.f32 (/.f32 (pow.f32 c #s(literal 6 binary32)) (+.f32 (pow.f32 c #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (.f32 c c)))) (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 c #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (.f32 c c)))))
(-.f32 (/.f32 (pow.f32 c #s(literal 4 binary32)) (fma.f32 c c #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 c c #s(literal 1 binary32))))
(-.f32 (*.f32 c c) #s(literal 1 binary32))
(fma.f32 (exp.f32 (log.f32 c)) (exp.f32 (log.f32 c)) #s(literal -1 binary32))
(fma.f32 (*.f32 c c) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 (+.f32 c #s(literal 1 binary32)) c (*.f32 (+.f32 c #s(literal 1 binary32)) #s(literal -1 binary32)))
(fma.f32 c (+.f32 c #s(literal 1 binary32)) (*.f32 #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))))
(fma.f32 c c #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 c c) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 c c #s(literal 1 binary32)) (-.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32))) #s(literal -1 binary32))
(pow.f32 (/.f32 (-.f32 (+.f32 (pow.f32 c #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (.f32 c c) #s(literal -1 binary32))) (+.f32 (pow.f32 c #s(literal 6 binary32)) #s(literal -1 binary32))) #s(literal -1 binary32))
(+.f32 (.f32 c (+.f32 c #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (+.f32 c #s(literal 1 binary32))))
(+.f32 (.f32 (+.f32 c #s(literal 1 binary32)) c) (.f32 (+.f32 c #s(literal 1 binary32)) #s(literal -1 binary32)))
(+.f32 (*.f32 c c) #s(literal -1 binary32))
(+.f32 #s(literal -1 binary32) (*.f32 c c))
(*.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32)))))
(*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32)) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal -1 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal -1 binary32) (PI.f32))))
(*.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) #s(literal 1/2 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (pow.f32 #s(literal 1 binary32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32))
(*.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 (neg.f32 (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 (neg.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal -1 binary32) (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 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(pow.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/4 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))) #s(literal -1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) #s(literal -1/6 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/4 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(fabs.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(exp.f32 (neg.f32 (log.f32 (sqrt.f32 (PI.f32)))))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal -1/2 binary32)))
(exp.f32 (*.f32 (neg.f32 (log.f32 (PI.f32))) #s(literal 1/2 binary32)))
(exp.f32 (*.f32 (log.f32 (sqrt.f32 (PI.f32))) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))

eval254.0ms (2.6%)

Memory: -20.4MiB live, 345.9MiB allocated
Compiler: Compiled 52 066 to 4 917 computations (90.6% saved)

prune46.0ms (0.5%)

Memory

15.5MiB live, 127.8MiB allocated

Pruning

30 alts after pruning (27 fresh and 3 done)

	Pruned	Kept	Total
New	1 028	15	1 043
Fresh	6	12	18
Picked	2	3	5
Done	0	0	0
Total	1 036	30	1 066

Accuracy

99.9%

Counts

1 066 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.2%	(/.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))))
▶	14.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	90.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	89.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))))) (*.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)))
	97.7%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	97.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) cosTheta)))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 (-.f32 c #s(literal 1 binary32)) #s(literal -1/2 binary32) #s(literal 1 binary32)) c) cosTheta (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (*.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	49.1%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	69.5%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (+.f32 c #s(literal 1 binary32))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	97.8%	(/.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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.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 (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)))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	94.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	94.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	90.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	90.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	32.7%	(-.f32 (/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (/.f32 (*.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))))
	13.2%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))) (*.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
	56.1%	(*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)))
	56.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))
	13.9%	(.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (PI.f32)) (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))))
▶	91.7%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 2 068 to 1 263 computations (38.9% saved)

simplify150.0ms (1.5%)

Memory

-1.3MiB live, 208.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f32 c c #s(literal -1 binary32))
cost-diff	160	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))))
cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
cost-diff	512	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))
cost-diff	0	(/.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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	192	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
cost-diff	192	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)))
cost-diff	0	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	192	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(PI.f32)
cost-diff	0	(sqrt.f32 (PI.f32))
cost-diff	0	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
cost-diff	0	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	352	(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	599
0	107	599
1	174	577
2	356	571
3	915	568
4	2199	552
5	5257	552
0	8196	518

Stop Event

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

Calls

Call 1

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

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

localize159.0ms (1.6%)

Memory

-24.0MiB live, 327.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3515625	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
accuracy	25.937658396211532	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))))
accuracy	30.5900379651434	(fma.f32 c c #s(literal -1 binary32))
accuracy	0.12175751953688403	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.22265625	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)))
accuracy	0.4088220337643558	(/.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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.6100132688607536	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.62890625	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	2.507633827136281	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
accuracy	0	(sqrt.f32 (PI.f32))
accuracy	0	(PI.f32)
accuracy	0.3515625	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	2.373908088771379	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.12175751953688403	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.22265625	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
accuracy	0.34375	(*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Samples

113.0ms	255×	0	valid
1.0ms	1×	1	valid

Compiler

Compiled 1 174 to 118 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-div: 30.0ms (33.3% of total)

ival-mult: 26.0ms (28.9% of total)

ival-sqrt: 9.0ms (10% of total)

ival-add: 8.0ms (8.9% of total)

ival-pow: 6.0ms (6.7% of total)

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

ival-sub: 3.0ms (3.3% of total)

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

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series149.0ms (1.5%)

Memory

9.2MiB live, 84.4MiB allocated

Counts

25 → 142

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
15.0ms	cosTheta	@	-inf	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI))))) (/ 1 (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI)))))) (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (+ (* c c) -1) (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta)))) (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (sqrt (/ 1 (PI))) cosTheta) (* cosTheta (sqrt (PI))))
7.0ms	c	@	0	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI))))) (/ 1 (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI)))))) (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (+ (* c c) -1) (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta)))) (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (sqrt (/ 1 (PI))) cosTheta) (* cosTheta (sqrt (PI))))
6.0ms	cosTheta	@	inf	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI))))) (/ 1 (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI)))))) (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (+ (* c c) -1) (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta)))) (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (sqrt (/ 1 (PI))) cosTheta) (* cosTheta (sqrt (PI))))
4.0ms	c	@	inf	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI))))) (/ 1 (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI)))))) (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (+ (* c c) -1) (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta)))) (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (sqrt (/ 1 (PI))) cosTheta) (* cosTheta (sqrt (PI))))
4.0ms	cosTheta	@	0	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI))))) (/ 1 (/ (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (* cosTheta (sqrt (PI)))))) (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (+ (* c c) -1) (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta)))) (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (/ (sqrt (/ 1 (PI))) cosTheta) (* cosTheta (sqrt (PI))))

simplify218.0ms (2.3%)

Memory

18.1MiB live, 228.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1016	9243
1	3355	8773
0	8340	8320

Stop Event

1×	iter limit
1×	node limit

Counts

142 → 141

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

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 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* cosTheta (sqrt (PI)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 (fma.f32 (neg.f32 (fma.f32 (-.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (PI.f32)) (.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) cosTheta (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 (fma.f32 (fma.f32 (neg.f32 (fma.f32 (fma.f32 (neg.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (-.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (PI.f32)) (.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))) (-.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) cosTheta (-.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (PI.f32)) (*.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))))))) cosTheta (neg.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (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 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (sqrt (PI)))))
(*.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* -1/2 (* (* cosTheta (+ (PI) (* -4 (PI)))) (sqrt (/ 1 (PI)))))))))
(.f32 (fma.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 (.f32 #s(literal -3 binary32) (PI.f32)) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI))))) (* -1/2 (* (* cosTheta (+ (* -8 (PI)) (* -1 (+ (PI) (* -4 (PI)))))) (sqrt (/ 1 (PI)))))))))))
(.f32 (fma.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3 binary32) (PI.f32) (.f32 (fma.f32 #s(literal -8 binary32) (PI.f32) (*.f32 #s(literal 3 binary32) (PI.f32))) cosTheta)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* (* cosTheta (- (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))) 1)) (sqrt (/ 1 (PI))))) cosTheta)
(/.f32 (*.f32 (fma.f32 (fma.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* (sqrt (/ 1 (PI))) (- (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))) 1)) (* (* cosTheta (- (/ 1 (- c 1)) (+ 1/2 (/ c (- c 1))))) (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 c #s(literal 1 binary32))) #s(literal 1/2 binary32)) (/.f32 c (-.f32 c #s(literal 1 binary32)))) cosTheta (fma.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)) #s(literal -1 binary32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* cosTheta (+ (* (sqrt (/ 1 (PI))) (- (/ 1 (- c 1)) (+ 1/2 (/ c (- c 1))))) (* (* cosTheta (- (* -1 (/ (- 1 c) (- c 1))) 1/2)) (sqrt (/ 1 (PI)))))) (* (sqrt (/ 1 (PI))) (- (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))) 1))))) cosTheta)
(/.f32 (fma.f32 cosTheta (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) c) (fma.f32 #s(literal -1 binary32) c #s(literal 1 binary32))) #s(literal 1/2 binary32)) cosTheta (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 c #s(literal 1 binary32))) #s(literal 1/2 binary32)) (/.f32 c (-.f32 c #s(literal 1 binary32)))))) cosTheta) (*.f32 (fma.f32 (fma.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* (* cosTheta (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))))) (sqrt (PI)))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 (/.f32 (fma.f32 c c #s(literal -1 binary32)) (-.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))) cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* (sqrt (PI)) (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))))) (* (* cosTheta (- (+ 1/2 (/ c (- c 1))) (+ (/ 1 (- c 1)) (/ (* (+ (* -1 (- c 1)) (* (sqrt (PI)) (- (pow c 2) 1))) (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))))) (- c 1))))) (sqrt (PI)))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* cosTheta (+ (* (sqrt (PI)) (- (+ 1/2 (/ c (- c 1))) (+ (/ 1 (- c 1)) (/ (* (+ (* -1 (- c 1)) (* (sqrt (PI)) (- (pow c 2) 1))) (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))))) (- c 1))))) (* (* cosTheta (- 1/2 (+ (* -1 (/ (- 1 c) (- c 1))) (+ (/ (* (+ (* -1 (- c 1)) (* (sqrt (PI)) (- (pow c 2) 1))) (- (+ 1/2 (/ c (- c 1))) (+ (/ 1 (- c 1)) (/ (* (+ (* -1 (- c 1)) (* (sqrt (PI)) (- (pow c 2) 1))) (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1))))) (- c 1))))) (- c 1)) (/ (* (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1)))) (- (+ 1 (* -1/2 (- c 1))) c)) (- c 1)))))) (sqrt (PI))))) (* (sqrt (PI)) (- 1 (* (sqrt (PI)) (/ (- (pow c 2) 1) (- c 1)))))))))
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(- c 1)
(-.f32 c #s(literal 1 binary32))
(- (+ c (* cosTheta (+ (* -1 (- c 1)) (* (sqrt (PI)) (- (pow c 2) 1))))) 1)
(fma.f32 (-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta (-.f32 c #s(literal 1 binary32)))
(- (+ c (* cosTheta (+ (* -1 (- c 1)) (+ (* cosTheta (- (+ 1 (* -1/2 (- c 1))) c)) (* (sqrt (PI)) (- (pow c 2) 1)))))) 1)
(fma.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 (-.f32 c #s(literal 1 binary32)) #s(literal -1/2 binary32) #s(literal 1 binary32)) c) cosTheta (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (-.f32 c #s(literal 1 binary32))) cosTheta (-.f32 c #s(literal 1 binary32)))
(- (+ c (* cosTheta (+ (* -1 (- c 1)) (+ (* cosTheta (- (+ 1 (+ (* -1/2 (- c 1)) (* cosTheta (+ (* -1 (- 1 c)) (* -1/2 (- c 1)))))) c)) (* (sqrt (PI)) (- (pow c 2) 1)))))) 1)
(fma.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 #s(literal -1/2 binary32) c #s(literal 1/2 binary32)) (-.f32 #s(literal 1 binary32) c)) cosTheta (fma.f32 (-.f32 c #s(literal 1 binary32)) #s(literal -1/2 binary32) #s(literal 1 binary32))) c) cosTheta (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (-.f32 c #s(literal 1 binary32))) cosTheta (-.f32 c #s(literal 1 binary32)))
1
#s(literal 1 binary32)
(+ 1 (* -2 cosTheta))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (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 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(fma.f32 (/.f32 (fma.f32 (/.f32 #s(literal -1/4 binary32) (.f32 (PI.f32) #s(literal -2 binary32))) (/.f32 (.f32 (pow.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) cosTheta) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32))) (.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (/.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))) #s(literal -1 binary32) (fma.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))))
(- (+ (* -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))))))))
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(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
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(* (sqrt (* cosTheta (PI))) (sqrt -1/2))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2)))))
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(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (+ (* 1/64 (/ (* cosTheta (PI)) (pow (sqrt -1/2) 2))) (* 1/16 (PI))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))))
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(* (sqrt (/ 1 (PI))) (/ (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) (- c 1)))
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(* (sqrt (PI)) (/ (- c 1) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2)))))))
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(fma.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 c #s(literal 1 binary32))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))))
(+ (* -1 (* (/ (+ (* -1/4 (/ (* cosTheta (pow (- c 1) 3)) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt -2) 2) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 3))))) (* -1/8 (* (sqrt (pow cosTheta 3)) (/ (pow (- c 1) 2) (* (exp (pow cosTheta 2)) (* (pow (sqrt -2) 3) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 2))))))) (pow cosTheta 4)) (sqrt (PI)))) (+ (* -1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (pow (- c 1) 2) (* (exp (pow cosTheta 2)) (* (sqrt -2) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 2)))))) (* (sqrt (PI)) (/ (- c 1) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2)))))))))
(-.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 c #s(literal 1 binary32))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))) (.f32 (/.f32 (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (pow.f32 cosTheta #s(literal 3 binary32)))) (/.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (/.f32 (.f32 #s(literal -1/4 binary32) (.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) cosTheta)) (.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal 2 binary32)) #s(literal -2 binary32)) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))) (sqrt.f32 (PI.f32))))
(+ (* -1 (* (/ (+ (* -1/2 (* (sqrt cosTheta) (/ (* (+ (* -1/4 (/ (* cosTheta (pow (- c 1) 3)) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt -2) 2) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 3))))) (* -1/8 (* (sqrt (pow cosTheta 3)) (/ (pow (- c 1) 2) (* (exp (pow cosTheta 2)) (* (pow (sqrt -2) 3) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 2))))))) (- c 1)) (* (exp (pow cosTheta 2)) (* (sqrt -2) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2)))))))))) (+ (* 1/16 (* (sqrt (pow cosTheta 5)) (/ (pow (- c 1) 2) (* (exp (pow cosTheta 2)) (* (pow (sqrt -2) 5) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 2)))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (- c 1) 3)) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt -2) 4) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 3))))))) (pow cosTheta 6)) (sqrt (PI)))) (+ (* -1 (* (/ (+ (* -1/4 (/ (* cosTheta (pow (- c 1) 3)) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt -2) 2) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 3))))) (* -1/8 (* (sqrt (pow cosTheta 3)) (/ (pow (- c 1) 2) (* (exp (pow cosTheta 2)) (* (pow (sqrt -2) 3) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 2))))))) (pow cosTheta 4)) (sqrt (PI)))) (+ (* -1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (pow (- c 1) 2) (* (exp (pow cosTheta 2)) (* (sqrt -2) (pow (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))) 2)))))) (* (sqrt (PI)) (/ (- c 1) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))))))))
(fma.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 cosTheta)) (.f32 (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (pow.f32 cosTheta #s(literal 3 binary32)))) (/.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (/.f32 (.f32 #s(literal -1/4 binary32) (.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) cosTheta)) (.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal 2 binary32)) #s(literal -2 binary32)) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))))) (.f32 #s(literal 1/16 binary32) (fma.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal 2 binary32)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 4 binary32)))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))) (.f32 (/.f32 (sqrt.f32 (pow.f32 cosTheta #s(literal 5 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32))))))) (pow.f32 cosTheta #s(literal 6 binary32))) (neg.f32 (/.f32 (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (pow.f32 cosTheta #s(literal 3 binary32)))) (/.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (/.f32 (.f32 #s(literal -1/4 binary32) (.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) cosTheta)) (.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal 2 binary32)) #s(literal -2 binary32)) (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))))) (fma.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (/.f32 (pow.f32 (-.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (pow.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)) (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 c #s(literal 1 binary32))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))))
(* cosTheta (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))))
(.f32 (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta)
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (- c 1) (* (exp (pow cosTheta 2)) (sqrt -2))))) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2)))))))
(.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (- c 1) (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (- c 1) (* (exp (pow cosTheta 2)) (sqrt -2))))) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2))))))))
(.f32 (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (- c 1) (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (- c 1) (* (exp (pow cosTheta 2)) (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (- c 1) (* (exp (pow cosTheta 2)) (sqrt -2))))) (+ (* (sqrt (PI)) (- (pow c 2) 1)) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -2) (- c 1)) (exp (pow cosTheta 2)))))))))
(.f32 (fma.f32 (.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (/.f32 (-.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))))) cosTheta)
(* -2 cosTheta)
(*.f32 #s(literal -2 binary32) cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta)
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (neg.f32 (.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 #s(literal -1 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(-.f32 (fma.f32 (.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))))) (.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(-.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (.f32 (.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))))) (.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
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c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (/ 1 c)))
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(/.f32 (fma.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (fma.f32 (/.f32 (-.f32 (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 c c)) (/.f32 (-.f32 (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) c)) #s(literal 1 binary32)) c)
(/ (+ 1 (+ (* -1 (* (/ (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (- (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) (pow c 2)) (sqrt (PI)))) (+ (* -1 (* (/ (+ (* -1 (* (/ (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (- (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) (* (/ (* (+ (* -1 (* cosTheta (sqrt (PI)))) (* -1 (* (/ 1 (exp (pow cosTheta 2))) (sqrt (- 1 (* 2 cosTheta)))))) (- (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))) cosTheta) (sqrt (/ 1 (PI))))) (pow c 3)) (sqrt (PI)))) (* (/ (- (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) c) (sqrt (PI)))))) c)
(/.f32 (fma.f32 (sqrt.f32 (PI.f32)) (+.f32 (neg.f32 (/.f32 (-.f32 (fma.f32 (/.f32 (-.f32 (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 c c))) (neg.f32 (/.f32 (fma.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))) (/.f32 (-.f32 (fma.f32 (/.f32 (-.f32 (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (.f32 (/.f32 (.f32 (-.f32 (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (neg.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (pow.f32 c #s(literal 3 binary32))))) (fma.f32 (/.f32 (-.f32 (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) c) (sqrt.f32 (PI.f32)) #s(literal 1 binary32))) c)
(* (* (pow c 2) cosTheta) (sqrt (PI)))
(.f32 (.f32 (*.f32 c c) cosTheta) (sqrt.f32 (PI.f32)))
(* (pow c 2) (+ (* cosTheta (sqrt (PI))) (* (/ 1 (* c (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))))
(.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) c))) (*.f32 c c))
(* (pow c 2) (+ (* -1 (* (/ 1 (* (pow c 2) (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ cosTheta (pow c 2)) (sqrt (PI)))) (+ (* cosTheta (sqrt (PI))) (* (/ 1 (* c (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))))))
(.f32 (-.f32 (fma.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 cosTheta (.f32 c c)) cosTheta) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) c))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (.f32 c c)))) (.f32 c c))
(pow c 2)
(*.f32 c c)
(* (pow c 2) (- 1 (/ 1 (pow c 2))))
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 c c))) (*.f32 c c))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(/.f32 (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (fma.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 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 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32) #s(literal 1 binary32)) c)
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (- (* (/ (- (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (sqrt (PI))) c) (sqrt (/ 1 (PI)))) 1)))
(.f32 (neg.f32 c) (fma.f32 (/.f32 (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (PI))) (- (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (sqrt (PI))))) (* (/ (+ (sqrt (PI)) (* -1 (sqrt (PI)))) c) (sqrt (/ 1 (PI))))) c)) 1)))
(.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (fma.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (/.f32 #s(literal 0 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (* c (- (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (PI))) (- (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (sqrt (PI))))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (PI))) (+ (sqrt (PI)) (* -1 (sqrt (PI)))))) (* -1 (* (/ (+ (sqrt (PI)) (* -1 (sqrt (PI)))) c) (sqrt (/ 1 (PI)))))) c))) c)) 1)))
(.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (fma.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 0 binary32) (/.f32 #s(literal 0 binary32) c))) c)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (/ (- (* (/ (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))) c) (sqrt (PI))) 1) c))
(/.f32 (fma.f32 (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) c) (sqrt.f32 (PI.f32)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))))) (* -1 (* (/ (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (* (/ (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))) c) (sqrt (PI))))) c)) 1) c))
(/.f32 (fma.f32 (/.f32 (neg.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (/.f32 (-.f32 (neg.f32 (fma.f32 (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (*.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)))) (neg.f32 c)) #s(literal -1 binary32) #s(literal 1 binary32)) c)
(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))))) (* -1 (/ (+ (* -1 (* (/ (+ (* (/ (* (+ (* -1 (* cosTheta (sqrt (PI)))) (* -1 (* (/ 1 (exp (pow cosTheta 2))) (sqrt (- 1 (* 2 cosTheta)))))) (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) cosTheta) (sqrt (/ 1 (PI)))) (* (/ (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (* (/ (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c) (sqrt (PI)))) (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (* (/ (- (sqrt (/ 1 (PI))) (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))) (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))) c))) c)) 1) c))
(/.f32 (fma.f32 (/.f32 (neg.f32 (fma.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (/.f32 (-.f32 (neg.f32 (fma.f32 (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (.f32 (.f32 (neg.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c) (-.f32 (neg.f32 (fma.f32 (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (*.f32 (PI.f32) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) c))) (neg.f32 c)) #s(literal -1 binary32) #s(literal 1 binary32)) c)
(* (pow c 2) (+ (* -1 (/ (+ (* -1 (* (/ 1 (exp (pow cosTheta 2))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (/ (+ (* -1 (* cosTheta (sqrt (PI)))) (* -1 (* (/ 1 (exp (pow cosTheta 2))) (sqrt (- 1 (* 2 cosTheta)))))) c))) c)) (* cosTheta (sqrt (PI)))))
(.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (/.f32 (-.f32 (/.f32 (neg.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta)))) (neg.f32 c)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta))) c)) (*.f32 c c))

rewrite383.0ms (4%)

Memory

6.6MiB live, 387.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	393
0	107	364
1	408	339
2	2863	334
0	9422	325

Stop Event

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

Counts

25 → 2 192

Calls

Call 1

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

Outputs
(*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (PI.f32)))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (neg.f32 cosTheta)))
(*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))
(.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
(.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))))
(.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
(*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))
(*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))
(.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)))
(/.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) cosTheta)
(/.f32 (pow.f32 (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal -1 binary32)) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (.f32 #s(literal -1 binary32) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
(/.f32 (.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (.f32 (neg.f32 (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)
(/.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) #s(literal -1 binary32)) (.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
(/.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (neg.f32 (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (neg.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
(/.f32 (neg.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (*.f32 (neg.f32 (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))) (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta)
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(pow.f32 (.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32))
(pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal -1 binary32))
(pow.f32 (.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal -1 binary32))
(pow.f32 (/.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) #s(literal -1 binary32))
(pow.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) #s(literal -1 binary32))
(exp.f32 (fma.f32 (neg.f32 cosTheta) cosTheta (.f32 (log.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal -1 binary32))))
(exp.f32 (fma.f32 (log.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal -1 binary32) (.f32 (neg.f32 cosTheta) cosTheta)))
(.f32 (/.f32 (.f32 (.f32 (-.f32 c #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 (.f32 (pow.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) #s(literal 2 binary32)) (PI.f32)) (pow.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))) #s(literal 2 binary32)))) (-.f32 (.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32)))))
(.f32 (/.f32 (.f32 (.f32 (-.f32 c #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 (pow.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) #s(literal 3 binary32)))) (fma.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))) (-.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))) (.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))) (.f32 (pow.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) #s(literal 2 binary32)) (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32)))) (-.f32 c #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32)))))) (pow.f32 (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (*.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32)))))) (.f32 (neg.f32 (*.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal 2 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta) #s(literal -3 binary32)) (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal -3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (-.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta) #s(literal -3 binary32)) (pow.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) #s(literal -3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (-.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))) (*.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))) (-.f32 c #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal 1 binary32)))
(*.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)))
(.f32 (pow.f32 (.f32 (.f32 (-.f32 c #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (*.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))) (pow.f32 (/.f32 (/.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 c #s(literal 1 binary32))) #s(literal 1 binary32)) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal 1 binary32))))) (pow.f32 (.f32 (*.f32 (-.f32 c #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
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eval545.0ms (5.6%)

Memory: -150.2MiB live, 588.8MiB allocated
Compiler: Compiled 84 033 to 8 828 computations (89.5% saved)

prune55.0ms (0.6%)

Memory

-3.5MiB live, 153.0MiB allocated

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	1 774	9	1 783
Fresh	10	12	22
Picked	3	2	5
Done	1	2	3
Total	1 788	25	1 813

Accuracy

100.0%

Counts

1 813 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.2%	(/.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))))
	90.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	91.1%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (-.f32 c #s(literal 1 binary32))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 (-.f32 (fma.f32 (-.f32 c #s(literal 1 binary32)) #s(literal -1/2 binary32) #s(literal 1 binary32)) c) cosTheta (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
▶	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (*.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
▶	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	90.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	94.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	90.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	90.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
▶	90.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	32.7%	(-.f32 (/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (/.f32 (*.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))))
	56.3%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta))))
	56.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))
	91.6%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
✓	91.7%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 1 740 to 1 074 computations (38.3% saved)

simplify124.0ms (1.3%)

Memory

14.7MiB live, 187.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f32 cosTheta)
cost-diff	0	(pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))
cost-diff	0	(+.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32)))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	160	(*.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))
cost-diff	192	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 (-.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)
cost-diff	0	#s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta))
cost-diff	64	(-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32)))
cost-diff	544	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
cost-diff	0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
cost-diff	0	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
cost-diff	0	#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
cost-diff	0	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	64	(-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))
cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	717
0	127	703
1	219	682
2	428	675
3	1322	672
4	5219	672
0	8170	638

Stop Event

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

Calls

Call 1

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

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

localize300.0ms (3.1%)

Memory

8.8MiB live, 245.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12175751953688403	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.22265625	(/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta))
accuracy	0.34375	(*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
accuracy	0.25	(/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.3515625	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	1.1855763817563592	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
accuracy	0.9339638183790943	(-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32)))
accuracy	1.3136080945609632	#s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta))
accuracy	1.5401307251903644	(fma.f32 c c #s(literal -1 binary32))
accuracy	20.330787967621923	(fma.f32 (-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta c)
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
accuracy	0.62890625	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	2.3673939057968423	#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
accuracy	0.08984375	(/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))
accuracy	0.22265625	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))))))
accuracy	0.34375	(*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))
accuracy	0.4088220337643558	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Samples

242.0ms	255×	0	valid
1.0ms	1×	1	valid

Compiler

Compiled 1 336 to 146 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 202.0ms

ival-div: 135.0ms (67% of total)

ival-mult: 21.0ms (10.4% of total)

ival-pow: 12.0ms (6% of total)

ival-add: 10.0ms (5% of total)

ival-sub: 8.0ms (4% of total)

ival-sqrt: 8.0ms (4% of total)

ival-exp: 4.0ms (2% of total)

ival-pi: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series77.0ms (0.8%)

Memory

-13.0MiB live, 30.1MiB allocated

Counts

31 → 176

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	cosTheta	@	0	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (- (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) 1) cosTheta) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* 1 (- 1 cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ 1 (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1))) (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1)) (pow (exp cosTheta) (neg cosTheta)) (exp cosTheta) (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta)))))) (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (/ (PI) (- 1 (- cosTheta (neg cosTheta)))) (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) (+ (* c c) -1) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (/ (* 1 (- 1 cosTheta)) (* (sqrt (PI)) cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta) (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (- (- 1 cosTheta) cosTheta))
18.0ms	cosTheta	@	-inf	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (- (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) 1) cosTheta) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* 1 (- 1 cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ 1 (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1))) (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1)) (pow (exp cosTheta) (neg cosTheta)) (exp cosTheta) (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta)))))) (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (/ (PI) (- 1 (- cosTheta (neg cosTheta)))) (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) (+ (* c c) -1) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (/ (* 1 (- 1 cosTheta)) (* (sqrt (PI)) cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta) (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (- (- 1 cosTheta) cosTheta))
5.0ms	cosTheta	@	inf	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (- (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) 1) cosTheta) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* 1 (- 1 cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ 1 (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1))) (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1)) (pow (exp cosTheta) (neg cosTheta)) (exp cosTheta) (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta)))))) (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (/ (PI) (- 1 (- cosTheta (neg cosTheta)))) (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) (+ (* c c) -1) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (/ (* 1 (- 1 cosTheta)) (* (sqrt (PI)) cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta) (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (- (- 1 cosTheta) cosTheta))
4.0ms	c	@	0	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (- (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) 1) cosTheta) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* 1 (- 1 cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ 1 (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1))) (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1)) (pow (exp cosTheta) (neg cosTheta)) (exp cosTheta) (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta)))))) (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (/ (PI) (- 1 (- cosTheta (neg cosTheta)))) (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) (+ (* c c) -1) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (/ (* 1 (- 1 cosTheta)) (* (sqrt (PI)) cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta) (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (- (- 1 cosTheta) cosTheta))
4.0ms	c	@	inf	((* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ 1 (/ (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (- c 1) (sqrt (PI))))) (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (- (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) 1) cosTheta) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* 1 (- 1 cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ 1 (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1))) (+ (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (+ c 1)) (pow (exp cosTheta) (neg cosTheta)) (exp cosTheta) (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta)))))) (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (/ (PI) (- 1 (- cosTheta (neg cosTheta)))) (+ (* (- (* (+ (* c c) -1) (sqrt (PI))) (- c 1)) cosTheta) c) (+ (* c c) -1) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (sqrt (PI)) cosTheta) (/ (* 1 (- 1 cosTheta)) (* (sqrt (PI)) cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta) (/ (pow (exp cosTheta) (neg cosTheta)) (* (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))) cosTheta)) (- (- 1 cosTheta) cosTheta))

simplify250.0ms (2.6%)

Memory

7.5MiB live, 165.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1086	8916
1	3520	8442
0	8552	8024

Stop Event

1×	iter limit
1×	node limit

Counts

176 → 175

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

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

rewrite275.0ms (2.8%)

Memory

7.9MiB live, 122.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	513
0	127	490
1	558	473
2	4656	461
0	8130	459

Stop Event

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

Counts

31 → 1 008

Calls

Call 1

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

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

eval432.0ms (4.5%)

Memory: 15.1MiB live, 168.5MiB allocated
Compiler: Compiled 46 357 to 5 345 computations (88.5% saved)

prune72.0ms (0.7%)

Memory

-29.9MiB live, 58.3MiB allocated

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	950	10	960
Fresh	7	9	16
Picked	4	1	5
Done	2	2	4
Total	963	22	985

Accuracy

100.0%

Counts

985 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.2%	(/.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))))
	91.1%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (* cosTheta (sqrt (PI)))) (* (- c 1) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)))) (-.f32 c #s(literal 1 binary32))) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (+.f32 (+.f32 (neg.f32 c) #s(literal 1 binary32)) (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 (fma.f32 (+.f32 (.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 (neg.f32 c) #s(literal 1 binary32))) cosTheta c) #s(literal 1 binary32)) cosTheta)) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	90.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (*.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (pow (exp cosTheta) (neg cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	90.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ 1 (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta))))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	93.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ 1 (* cosTheta (sqrt (/ (PI) (- 1 (- cosTheta (neg cosTheta))))))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	90.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	91.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	32.7%	(-.f32 (/.f32 (+.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32))) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))) (/.f32 (*.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 3 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)))))
	56.3%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta))))
	56.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))
	55.9%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (*.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal -2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
	90.8%	(.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (PI.f32)) #s(approx (+ ( (+ (* c c) -1) (sqrt (PI))) (* (- c 1) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (*.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal 1 binary32))) cosTheta (-.f32 c #s(literal 1 binary32))) cosTheta))))
	91.6%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
✓	91.7%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 2 882 to 894 computations (69% saved)

regimes125.0ms (1.3%)

Memory

-10.9MiB live, 147.7MiB allocated

Counts

58 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

29.0ms	cosTheta
23.0ms	c
22.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
20.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
15.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta`
98.2%	1	`c`
98.2%	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)))))`
98.2%	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))))`
98.2%	1	`(+.f32 #s(literal 1 binary32) c)`
98.2%	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 72 to 58 computations (19.4% saved)

regimes64.0ms (0.7%)

Memory

14.1MiB live, 91.3MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

13.0ms	(+.f32 #s(literal 1 binary32) c)
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta`
98.2%	1	`c`
98.2%	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)))))`
98.2%	1	`(+.f32 #s(literal 1 binary32) c)`
98.2%	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))))`
98.2%	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 72 to 58 computations (19.4% saved)

regimes96.0ms (1%)

Memory

2.6MiB live, 82.7MiB allocated

Counts

31 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

36.0ms	c
24.0ms	(+.f32 #s(literal 1 binary32) c)
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
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
98.2%	1	`cosTheta`
98.2%	1	`c`
98.2%	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)))))`
98.2%	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))))`
98.2%	1	`(+.f32 #s(literal 1 binary32) c)`
98.2%	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 72 to 58 computations (19.4% saved)

regimes82.0ms (0.8%)

Memory

1.3MiB live, 78.0MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

34.0ms	(+.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))))
17.0ms	(+.f32 #s(literal 1 binary32) c)
7.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
7.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
7.0ms	c

Results

Accuracy	Segments	Branch
97.6%	1	`c`
97.6%	1	`(+.f32 #s(literal 1 binary32) c)`
97.6%	1	`cosTheta`
97.6%	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)))))`
97.6%	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))))`
97.6%	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)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes70.0ms (0.7%)

Memory

-14.0MiB live, 67.7MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

22.0ms	cosTheta
17.0ms	(+.f32 #s(literal 1 binary32) c)
7.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
7.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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)))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes38.0ms (0.4%)

Memory

-1.6MiB live, 37.6MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

19.0ms	cosTheta
4.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms	(/.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

Results

Accuracy	Segments	Branch
93.6%	1	`cosTheta`
93.6%	1	`c`
93.6%	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)))))`
93.6%	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))))`
93.6%	1	`(+.f32 #s(literal 1 binary32) c)`
93.6%	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)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes20.0ms (0.2%)

Memory

27.5MiB live, 27.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
91.7%	1	`cosTheta`
91.7%	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)))))`
91.7%	1	`c`
91.7%	1	`(+.f32 #s(literal 1 binary32) c)`
91.7%	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))))`
91.7%	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 72 to 58 computations (19.4% saved)

regimes18.0ms (0.2%)

Memory

-21.7MiB live, 17.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
5.0%	1	`cosTheta`
5.0%	1	`c`
5.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
5.0%	1	`(+.f32 #s(literal 1 binary32) c)`
5.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
5.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify103.0ms (1.1%)

Memory

-2.4MiB live, 77.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	216
1	110	215
2	128	215
3	172	215
4	252	215
5	385	215
6	535	215
7	717	215
8	814	215
9	861	215
10	881	215
11	907	215
12	930	215
13	950	215
14	965	215
15	986	215
16	1007	215
17	1022	215
18	1028	215
19	1029	215

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness957.0ms (9.9%)

Memory

22.8MiB live, 896.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	407	3010
1	1237	2916
2	4721	2838
0	8274	2706
0	60	395
0	102	374
1	384	349
2	3048	344
0	8102	337
0	18	73
0	33	73
1	141	66
2	1060	61
0	8551	61
0	63	393
0	107	364
1	408	339
2	2863	334
0	9422	325
0	78	513
0	127	490
1	558	473
2	4656	461
0	8130	459
0	1086	8916
1	3520	8442
0	8552	8024

Stop Event

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

Compiler

Compiled 1 020 to 484 computations (52.5% saved)

preprocess59.0ms (0.6%)

Memory: 0.8MiB live, 118.1MiB allocated
Compiler: Compiled 480 to 192 computations (60% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze26.0ms (0.3%)

sample2.2s (22.9%)

explain446.0ms (4.6%)

preprocess209.0ms (2.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify139.0ms (1.4%)

localize160.0ms (1.7%)

series39.0ms (0.4%)

simplify164.0ms (1.7%)

rewrite189.0ms (2%)

eval86.0ms (0.9%)

prune31.0ms (0.3%)

simplify177.0ms (1.8%)

localize178.0ms (1.8%)

series102.0ms (1.1%)

simplify215.0ms (2.2%)

rewrite165.0ms (1.7%)

eval254.0ms (2.6%)

prune46.0ms (0.5%)

simplify150.0ms (1.5%)

localize159.0ms (1.6%)

series149.0ms (1.5%)

simplify218.0ms (2.3%)

rewrite383.0ms (4%)

eval545.0ms (5.6%)

prune55.0ms (0.6%)

simplify124.0ms (1.3%)

localize300.0ms (3.1%)

series77.0ms (0.8%)

simplify250.0ms (2.6%)

rewrite275.0ms (2.8%)

eval432.0ms (4.5%)

prune72.0ms (0.7%)

regimes125.0ms (1.3%)

regimes64.0ms (0.7%)

regimes96.0ms (1%)

regimes82.0ms (0.8%)

regimes70.0ms (0.7%)

regimes38.0ms (0.4%)

regimes20.0ms (0.2%)

regimes18.0ms (0.2%)

simplify103.0ms (1.1%)

soundness957.0ms (9.9%)

preprocess59.0ms (0.6%)

end0.0ms (0%)

Profiling