Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze32.0ms (0.3%)

Memory

-6.5MiB live, 35.5MiB 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)

sample2.1s (21.8%)

Memory

-8.2MiB live, 2 781.5MiB allocated

Samples

1.7s	8 256×	0	valid
10.0ms	59×	0	invalid

Precisions

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

ival-pi: 303.0ms (21.3% of total)

ival-mult: 185.0ms (13% of total)

ival-div: 182.0ms (12.8% of total)

const: 138.0ms (9.7% of total)

ival-sqrt: 130.0ms (9.2% of total)

ival-<: 120.0ms (8.5% of total)

ival-add: 98.0ms (6.9% of total)

ival-exp: 98.0ms (6.9% of total)

ival-sub: 74.0ms (5.2% of total)

ival-neg: 47.0ms (3.3% of total)

ival-and: 25.0ms (1.8% of total)

exact: 15.0ms (1.1% of total)

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

Bogosity

explain362.0ms (3.7%)

Memory

6.5MiB live, 292.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

144.0ms

512×

valid

Compiler

Compiled 407 to 76 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 126.0ms

ival-sqrt: 49.0ms (38.9% of total)

ival-neg: 42.0ms (33.3% of total)

ival-div: 10.0ms (7.9% of total)

ival-mult: 9.0ms (7.1% of total)

ival-add: 5.0ms (4% of total)

ival-sub: 5.0ms (4% of total)

ival-exp: 4.0ms (3.2% of total)

ival-pi: 2.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess251.0ms (2.6%)

Memory

-16.9MiB live, 136.2MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.6%	(/.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

▶

97.6%

(/.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)

simplify137.0ms (1.4%)

Memory

-1.1MiB live, 73.2MiB 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)

localize99.0ms (1%)

Memory

17.7MiB live, 100.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.078125	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.37022713957955644	(/.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	0.5879288086106522	(*.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

59.0ms

256×

valid

Compiler

Compiled 254 to 38 computations (85% saved)

Precisions

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

ival-sqrt: 32.0ms (63.7% of total)

ival-div: 5.0ms (9.9% of total)

ival-mult: 4.0ms (8% of total)

ival-add: 3.0ms (6% of total)

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

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

ival-pi: 1.0ms (2% of total)

ival-neg: 1.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.3%)

Memory

-18.5MiB live, 55.2MiB 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
9.0ms	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))
3.0ms	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))
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))

simplify293.0ms (3%)

Memory

14.2MiB live, 295.1MiB 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)))

rewrite153.0ms (1.6%)

Memory

16.7MiB live, 250.4MiB 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))))

eval73.0ms (0.7%)

Memory: -27.0MiB live, 175.8MiB allocated
Compiler: Compiled 21 227 to 2 805 computations (86.8% saved)

prune25.0ms (0.3%)

Memory

33.6MiB live, 72.9MiB allocated

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	490	19	509
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	491	19	510

Accuracy

99.9%

Counts

510 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	58.5%	(/.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))))
	13.0%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.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)))))
	13.9%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) c) (/.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) c) (sqrt.f32 (PI.f32)))))
▶	98.1%	(/.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)))))
	49.6%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 #s(literal 1 binary32) 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)))))
▶	98.1%	(/.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)))))
▶	97.8%	(/.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 (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 (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)))))
▶	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.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)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.2%	(/.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)))))
	97.7%	(/.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)))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (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)))
	34.7%	(-.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)))))
	58.4%	(-.f32 (/.f32 (+.f32 c #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 (/.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)))))
	58.5%	(*.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)))
▶	5.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	92.4%	#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 1 352 to 764 computations (43.5% saved)

simplify121.0ms (1.2%)

Memory

-12.3MiB live, 147.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	192	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))
cost-diff	192	(+.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))))
cost-diff	192	(/.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))))
cost-diff	224	(*.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)))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	192	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
cost-diff	192	(+.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))))
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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	64	(.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) 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 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.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)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	160	(*.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))))
cost-diff	192	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
cost-diff	192	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.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)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	583
0	98	583
1	171	557
2	344	550
3	747	547
4	1471	547
5	2967	547
6	5401	547
0	8380	512

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

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

localize216.0ms (2.2%)

Memory

7.4MiB live, 277.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(*.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)))
accuracy	0.109375	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
accuracy	0.37022713957955644	(/.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)))))
accuracy	0.40234375	(/.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))))
accuracy	0.02734375	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
accuracy	0.078125	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.37022713957955644	(/.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)))))
accuracy	0.421875	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	0.078125	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.37022713957955644	(/.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)))))
accuracy	0.5	(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
accuracy	0.79296875	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	0	(/.f32 #s(literal 1 binary32) c)
accuracy	30.36938330255459	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy	0.078125	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.31640625	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
accuracy	0.3203125	(*.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))))
accuracy	0.37022713957955644	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.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)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Samples

105.0ms

256×

valid

Compiler

Compiled 1 164 to 110 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-div: 26.0ms (33.6% of total)

ival-mult: 13.0ms (16.8% of total)

ival-pow: 11.0ms (14.2% of total)

ival-add: 8.0ms (10.4% of total)

ival-sqrt: 5.0ms (6.5% of total)

ival-exp: 4.0ms (5.2% of total)

const: 4.0ms (5.2% of total)

ival-cbrt: 2.0ms (2.6% of total)

ival-sub: 2.0ms (2.6% of total)

ival-pi: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series260.0ms (2.7%)

Memory

-32.2MiB live, 378.7MiB allocated

Counts

23 → 210

Calls

Call 1

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

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(* (/ 1 cosTheta) (cbrt (/ 1 (PI))))
(/ (+ (cbrt (/ 1 (PI))) (* -1 (* cosTheta (cbrt (/ 1 (PI)))))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (cbrt (/ 1 (PI))) (* cosTheta (+ (* -1 (cbrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (cbrt (/ 1 (PI)))) (* -1/2 (* cosTheta (cbrt (/ 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)))
(* 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 (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 (* cosTheta (+ 1 c)))
(/ (+ (* -1 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (* -3/2 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (* cosTheta (- (* 1/2 (/ cosTheta (+ 1 c))) (* 3/2 (/ 1 (+ 1 c))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* (sqrt (/ 1 (PI))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))) (* (sqrt (/ 1 (PI))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) cosTheta)
(/ (+ (* cosTheta (- (sqrt (PI)) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (+ (sqrt (PI)) (* -3/2 (/ cosTheta (+ 1 c)))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (+ (sqrt (PI)) (* cosTheta (- (* 1/2 (/ cosTheta (+ 1 c))) (* 3/2 (/ 1 (+ 1 c)))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (PI))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (sqrt (PI)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* cosTheta (+ (* -1 (* (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) (sqrt (PI)))) (* (sqrt (PI)) (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))))))))))
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(* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2))))
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(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* (sqrt (/ 1 cosTheta)) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))
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(* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (* (exp (pow cosTheta 2)) (+ 1 c))))))))
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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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Calls

6 calls:

Time	Variable		Point	Expression
76.0ms	cosTheta	@	0	((+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))))
44.0ms	cosTheta	@	inf	((+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))))
39.0ms	c	@	-inf	((+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))))
39.0ms	c	@	inf	((+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))))
33.0ms	cosTheta	@	-inf	((+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))))

simplify304.0ms (3.1%)

Memory

24.4MiB live, 339.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1114	12100
1	3547	10773
0	8510	10340

Stop Event

1×	iter limit
1×	node limit

Counts

210 → 209

Calls

Call 1

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

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

rewrite270.0ms (2.8%)

Memory

1.1MiB live, 281.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	389
0	98	408
1	410	346
2	3316	346
0	8641	339

Stop Event

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

Counts

23 → 1 295

Calls

Call 1

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

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

eval251.0ms (2.6%)

Memory: 9.5MiB live, 351.0MiB allocated
Compiler: Compiled 54 708 to 6 382 computations (88.3% saved)

prune49.0ms (0.5%)

Memory

3.4MiB live, 156.2MiB allocated

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1 301	12	1 313
Fresh	9	5	14
Picked	3	2	5
Done	0	0	0
Total	1 313	19	1 332

Accuracy

99.9%

Counts

1 332 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	58.5%	(/.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))))
	95.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
▶	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.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 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	95.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) c))) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	85.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	97.8%	(/.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)))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.8%	(/.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)))))
	98.2%	(/.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)))))
▶	97.7%	(/.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)))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	58.3%	(*.f32 (/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (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)))))
	58.5%	(*.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)))
	57.9%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (/.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (PI.f32)))) (-.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) (neg.f32 cosTheta)))))
	95.3%	#s(approx (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (fma.f32 cosTheta c cosTheta) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))) (sqrt.f32 (PI.f32)))) cosTheta))
▶	92.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.1%	#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 1 285 to 781 computations (39.2% saved)

simplify153.0ms (1.6%)

Memory

3.3MiB live, 180.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32))))
cost-diff	64	(/.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)))
cost-diff	192	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))
cost-diff	320	(*.f32 (/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (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)))))
cost-diff	0	(+.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))))
cost-diff	0	(/.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)))))
cost-diff	64	(.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)))
cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))
cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))
cost-diff	160	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.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 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
cost-diff	192	(/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.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 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
cost-diff	0	(PI.f32)
cost-diff	0	(sqrt.f32 (PI.f32))
cost-diff	0	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
cost-diff	0	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
cost-diff	0	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (sqrt.f32 (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 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	192	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	646
0	107	648
1	185	620
2	407	613
3	1126	612
4	3965	612
5	7109	612
0	8030	575

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

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

localize401.0ms (4.1%)

Memory

-15.3MiB live, 300.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12337875976844202	(/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32)))
accuracy	0.25228500976844204	(pow.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))) #s(literal 2 binary32))
accuracy	1.0105590578344599	(/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32))))
accuracy	11.823658618227919	(*.f32 (/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (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)))))
accuracy	0.078125	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.37022713957955644	(/.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)))))
accuracy	0.5286712890737681	(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))
accuracy	0.79296875	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	0.109375	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
accuracy	0.37022713957955644	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.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 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
accuracy	0.40234375	(/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.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 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
accuracy	2.2004934698175522	#s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))
accuracy	0	(sqrt.f32 (PI.f32))
accuracy	0	(PI.f32)
accuracy	0.40625	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	2.109331395683796	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.078125	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.3359375	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.37022713957955644	(/.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 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.40625	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

301.0ms

256×

valid

Compiler

Compiled 1 269 to 121 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 280.0ms

ival-pow: 193.0ms (68.9% of total)

ival-mult: 32.0ms (11.4% of total)

ival-div: 23.0ms (8.2% of total)

ival-add: 7.0ms (2.5% of total)

ival-exp: 5.0ms (1.8% of total)

ival-sqrt: 5.0ms (1.8% of total)

ival-sub: 4.0ms (1.4% of total)

const: 4.0ms (1.4% of total)

ival-cbrt: 2.0ms (0.7% of total)

ival-pow2: 2.0ms (0.7% of total)

ival-pi: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

exact: 0.0ms (0% of total)

series146.0ms (1.5%)

Memory

-6.3MiB live, 241.9MiB allocated

Counts

25 → 227

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
23.0ms	c	@	0	((+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ 1 (+ c 1)) (sqrt (PI))) (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (sqrt (PI)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (- 1 cosTheta) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2) (/ (sqrt (PI)) (+ c 1)))
22.0ms	cosTheta	@	inf	((+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ 1 (+ c 1)) (sqrt (PI))) (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (sqrt (PI)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (- 1 cosTheta) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2) (/ (sqrt (PI)) (+ c 1)))
22.0ms	c	@	-inf	((+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ 1 (+ c 1)) (sqrt (PI))) (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (sqrt (PI)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (- 1 cosTheta) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2) (/ (sqrt (PI)) (+ c 1)))
20.0ms	cosTheta	@	0	((+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ 1 (+ c 1)) (sqrt (PI))) (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (sqrt (PI)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (- 1 cosTheta) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2) (/ (sqrt (PI)) (+ c 1)))
19.0ms	c	@	inf	((+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ 1 (+ c 1)) (sqrt (PI))) (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (sqrt (PI)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) (/ (/ (sqrt (PI)) (+ c 1)) (- (PI) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2))) (- (- 1 cosTheta) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (/ (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (+ c 1)) 2) (/ (sqrt (PI)) (+ c 1)))

simplify264.0ms (2.7%)

Memory

9.1MiB live, 316.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1546	18881
1	5154	17675
0	8221	17135

Stop Event

1×	iter limit
1×	node limit

Counts

227 → 226

Calls

Call 1

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

rewrite231.0ms (2.4%)

Memory

36.1MiB live, 295.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	440
0	107	423
1	441	408
2	3755	408
0	8364	403

Stop Event

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

Counts

25 → 885

Calls

Call 1

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

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

eval274.0ms (2.8%)

Memory: 7.1MiB live, 450.0MiB allocated
Compiler: Compiled 83 470 to 6 873 computations (91.8% saved)

prune47.0ms (0.5%)

Memory

-10.0MiB live, 156.2MiB allocated

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	1 541	14	1 555
Fresh	6	6	12
Picked	2	3	5
Done	0	2	2
Total	1 549	25	1 574

Accuracy

100.0%

Counts

1 574 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	58.0%	(/.f32 (.f32 (-.f32 (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)))) (sqrt.f32 (PI.f32))) (.f32 (-.f32 (PI.f32) (pow.f32 (*.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) #s(literal -2 binary32))) (+.f32 c #s(literal 1 binary32))))
	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)) (+.f32 c #s(literal 1 binary32)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
▶	95.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32)))))
	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
	88.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (-.f32 (sqrt.f32 (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) c)))))
	85.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (sqrt.f32 (PI.f32)))))
	95.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) c))) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
▶	85.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
✓	97.8%	(/.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)))))
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (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 (/.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)))))
✓	97.7%	(/.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)))))
▶	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	57.5%	(*.f32 (/.f32 (/.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal 2 binary32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (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)))))
	58.2%	(.f32 (/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))))
	55.0%	(*.f32 (/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))))
	58.1%	(.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (/.f32 (-.f32 (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 (PI.f32) (pow.f32 (.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) #s(literal -2 binary32)))))
	95.3%	#s(approx (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (fma.f32 cosTheta c cosTheta) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))) (sqrt.f32 (PI.f32)))) cosTheta))
	95.4%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (PI.f32) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
	92.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
✓	92.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.1%	#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 1 750 to 1 076 computations (38.5% saved)

simplify113.0ms (1.2%)

Memory

-22.0MiB live, 110.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.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 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	64	(-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))
cost-diff	64	(.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
cost-diff	160	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
cost-diff	192	(/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
cost-diff	0	(+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta))))
cost-diff	160	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
cost-diff	160	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
cost-diff	192	(/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.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)) (* (sqrt (PI)) cosTheta)) (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)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) 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 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	64	(.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff	160	(*.f32 (PI.f32) (log.f32 (E.f32)))
cost-diff	3200	(log.f32 (E.f32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	669
0	114	656
1	197	607
2	364	598
3	864	595
4	2320	595
5	4398	595
6	6547	595
0	8081	571

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

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

localize385.0ms (4%)

Memory

18.0MiB live, 296.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0625	(/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32))
accuracy	0.37022713957955644	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.5	(/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32))) cosTheta)
accuracy	0.79296875	(sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32)))
accuracy	0.109375	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
accuracy	0.37022713957955644	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
accuracy	0.40234375	(/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
accuracy	1.07382348293797	#s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
accuracy	0.37022713957955644	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
accuracy	0.40234375	(/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
accuracy	2.204148235183279	#s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))
accuracy	7.3092825229627	(fma.f32 cosTheta c cosTheta)
accuracy	0.37022713957955644	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
accuracy	0.5703125	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	2.0888326676888496	#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
accuracy	0.3359375	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
accuracy	0.37022713957955644	(/.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 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.40625	(.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta)
accuracy	1.0	(log.f32 (E.f32))

Samples

340.0ms

256×

valid

Compiler

Compiled 1 270 to 124 computations (90.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 312.0ms

ival-mult: 237.0ms (75.9% of total)

ival-div: 30.0ms (9.6% of total)

ival-sqrt: 11.0ms (3.5% of total)

ival-add: 8.0ms (2.6% of total)

ival-pow: 6.0ms (1.9% of total)

ival-sub: 5.0ms (1.6% of total)

ival-exp: 4.0ms (1.3% of total)

ival-pi: 3.0ms (1% of total)

ival-e: 3.0ms (1% of total)

ival-log: 3.0ms (1% of total)

ival-neg: 1.0ms (0.3% of total)

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

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

exact: 0.0ms (0% of total)

series177.0ms (1.8%)

Memory

9.8MiB live, 120.2MiB allocated

Counts

27 → 242

Calls

Call 1

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

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (* (PI) (log (E))))))
(/ (+ (sqrt (/ 1 (* (PI) (log (E))))) (* -1 (* cosTheta (sqrt (/ 1 (* (PI) (log (E)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (* (PI) (log (E))))) (* cosTheta (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* cosTheta (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (* (PI) (log (E))))) (* cosTheta (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* cosTheta (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (+ (* -1/2 (sqrt (/ 1 (* (PI) (log (E)))))) (* cosTheta (+ (sqrt (/ 1 (* (PI) (log (E))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E)))))))))))))) cosTheta)
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (+ (sqrt (* (PI) (log (E)))) (* -1 (* cosTheta (* (PI) (* (log (E)) (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E))))))))))))))
(* cosTheta (+ (sqrt (* (PI) (log (E)))) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (* (pow (PI) 3) (pow (log (E)) 3))) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E)))))))) 2))) (* (PI) (* (log (E)) (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E)))))))))))) (* (PI) (* (log (E)) (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E))))))))))))))
(* cosTheta (+ (sqrt (* (PI) (log (E)))) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (* (PI) (log (E)))) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E)))))))) (+ (* -1 (* (sqrt (* (pow (PI) 3) (pow (log (E)) 3))) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E)))))))) 2))) (* (PI) (* (log (E)) (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E))))))))))))) (+ (* -1 (* (sqrt (* (pow (PI) 3) (pow (log (E)) 3))) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E)))))))) (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E)))))))))) (* (PI) (* (log (E)) (+ (sqrt (/ 1 (* (PI) (log (E))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E))))))))))))) (+ (* -1 (* (sqrt (* (pow (PI) 3) (pow (log (E)) 3))) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E)))))))) 2))) (* (PI) (* (log (E)) (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (sqrt (/ 1 (* (PI) (log (E)))))))))))) (* (PI) (* (log (E)) (+ 1 (+ c (* -1 (sqrt (/ 1 (* (PI) (log (E))))))))))))))
(* 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))) (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* (sqrt (/ 1 (PI))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))) (* (sqrt (/ 1 (PI))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (PI))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (sqrt (PI)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* cosTheta (+ (* -1 (* (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) (sqrt (PI)))) (* (sqrt (PI)) (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))))))))))
(/ 1 (* cosTheta (+ 1 c)))
(/ (+ (* cosTheta (- (sqrt (PI)) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (+ (sqrt (PI)) (* -3/2 (/ cosTheta (+ 1 c)))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (+ (sqrt (PI)) (* cosTheta (- (* 1/2 (/ cosTheta (+ 1 c))) (* 3/2 (/ 1 (+ 1 c)))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* -1 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (* -3/2 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (* cosTheta (- (* 1/2 (/ cosTheta (+ 1 c))) (* 3/2 (/ 1 (+ 1 c))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (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))
(/ (+ (sqrt (/ 1 (* (PI) (log (E))))) (* cosTheta (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (* cosTheta (sqrt (/ 1 (* (PI) (log (E)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (* (PI) (log (E))))) (* cosTheta (+ (* -1 (sqrt (/ 1 (* (PI) (log (E)))))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (* (PI) (log (E)))))) (* -1/2 (* cosTheta (sqrt (/ 1 (* (PI) (log (E)))))))))))) cosTheta)
(* cosTheta (+ 1 c))
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (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)
(/ 1 (PI))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(* (sqrt (/ 1 (* cosTheta (* (PI) (log (E)))))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (* (PI) (log (E)))))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (* (PI) (log (E)))))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (* (PI) (log (E)))))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (* (PI) (log (E)))))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (* (PI) (log (E)))))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
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(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
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(* -1 (/ (- (* (/ (+ (sqrt (/ 1 (PI))) (* (/ 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 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))) c) (sqrt (PI)))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta)))))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (/ 1 (PI))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ 1 (* cosTheta (* (PI) (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))))) c) (sqrt (PI)))) c))) c)) 1) c))
(* -1 (/ (+ (* -1 (sqrt (PI))) (* (/ 1 c) (sqrt (PI)))) c))
(* -1 (/ (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (* -1 (sqrt (PI))) (* (/ 1 c) (sqrt (PI)))) c))) c))
(* -1 (/ (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (* -1 (sqrt (PI))) (* (/ 1 c) (sqrt (PI)))) c))) c))) c))
(+ (sqrt (PI)) (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) c)))
(+ (sqrt (PI)) (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) c))) c)))
(* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) c))
(* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) c))) c))
(* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (- 1 (* 2 cosTheta))))) (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (- 1 (* 2 cosTheta))))) c))) c))) c))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ cosTheta c)))))

Calls

6 calls:

Time	Variable		Point	Expression
99.0ms	cosTheta	@	0	((log (E)) (* (PI) (log (E))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (* (sqrt (* (PI) (log (E)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (+ (* cosTheta c) cosTheta) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (/ (- 1 (- cosTheta (neg cosTheta))) (PI)))
25.0ms	c	@	0	((log (E)) (* (PI) (log (E))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (* (sqrt (* (PI) (log (E)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (+ (* cosTheta c) cosTheta) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (/ (- 1 (- cosTheta (neg cosTheta))) (PI)))
21.0ms	cosTheta	@	inf	((log (E)) (* (PI) (log (E))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (* (sqrt (* (PI) (log (E)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (+ (* cosTheta c) cosTheta) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (/ (- 1 (- cosTheta (neg cosTheta))) (PI)))
17.0ms	cosTheta	@	-inf	((log (E)) (* (PI) (log (E))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (* (sqrt (* (PI) (log (E)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (+ (* cosTheta c) cosTheta) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (/ (- 1 (- cosTheta (neg cosTheta))) (PI)))
3.0ms	c	@	inf	((log (E)) (* (PI) (log (E))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (sqrt (PI))) (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI)))) (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (- 1 (- cosTheta (neg cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (* (sqrt (* (PI) (log (E)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (+ (* cosTheta c) cosTheta) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) (/ (sqrt (/ (- 1 (- cosTheta (neg cosTheta))) (PI))) cosTheta) (/ (- 1 (- cosTheta (neg cosTheta))) (PI)))

simplify262.0ms (2.7%)

Memory

-38.9MiB live, 210.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1359	14942
1	4410	13142
0	9003	12603

Stop Event

1×	iter limit
1×	node limit

Counts

242 → 240

Calls

Call 1

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

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

rewrite302.0ms (3.1%)

Memory

26.8MiB live, 217.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	501
0	114	473
1	483	441
2	3307	441
0	8757	436

Stop Event

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

Counts

27 → 917

Calls

Call 1

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

Outputs
#s(literal 1 binary32)
(log.f32 (exp.f32 (PI.f32)))
(*.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 5 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(*.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 4 binary32))) (cbrt.f32 (PI.f32)))
(*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(.f32 (cbrt.f32 (pow.f32 (.f32 (PI.f32) (cbrt.f32 (PI.f32))) #s(literal 2 binary32))) (cbrt.f32 (cbrt.f32 (PI.f32))))
(*.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32))) (cbrt.f32 (sqrt.f32 (PI.f32))))
(*.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (cbrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))))
(*.f32 (exp.f32 (log.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))) (exp.f32 (log.f32 (cbrt.f32 (PI.f32)))))
(.f32 (pow.f32 (pow.f32 (.f32 (PI.f32) (cbrt.f32 (PI.f32))) #s(literal 2 binary32)) #s(literal 1/3 binary32)) (cbrt.f32 (cbrt.f32 (PI.f32))))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32)) #s(literal 1/3 binary32)) (cbrt.f32 (sqrt.f32 (PI.f32))))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1/3 binary32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 5 binary32)) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 4 binary32)) #s(literal 1/2 binary32)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (cbrt.f32 (PI.f32))) #s(literal 3 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal 2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (cbrt.f32 (PI.f32)))
(.f32 (cbrt.f32 (PI.f32)) (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (PI.f32))))
(.f32 (cbrt.f32 (PI.f32)) (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (PI.f32)) #s(literal 1/2 binary32)))
(*.f32 (cbrt.f32 (PI.f32)) (log.f32 (exp.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))))
(*.f32 (cbrt.f32 (PI.f32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))
(*.f32 (sqrt.f32 (PI.f32)) (log.f32 (exp.f32 (sqrt.f32 (PI.f32)))))
(*.f32 (sqrt.f32 (PI.f32)) (sqrt.f32 (PI.f32)))
(*.f32 #s(literal 1 binary32) (PI.f32))
(*.f32 (PI.f32) (pow.f32 #s(literal 1 binary32) #s(literal 1/3 binary32)))
(*.f32 (PI.f32) #s(literal 1 binary32))
(cbrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))
(sqrt.f32 (*.f32 (PI.f32) (PI.f32)))
(/.f32 (neg.f32 (neg.f32 (PI.f32))) #s(literal 1 binary32))
(/.f32 (neg.f32 (PI.f32)) #s(literal -1 binary32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))
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(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 4 binary32) (.f32 cosTheta cosTheta))) #s(literal -1 binary32)) (.f32 (fma.f32 #s(literal 2 binary32) cosTheta #s(literal 1 binary32)) (neg.f32 (PI.f32))))
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(/.f32 (-.f32 (neg.f32 (PI.f32)) (.f32 (neg.f32 (PI.f32)) (.f32 #s(literal 2 binary32) cosTheta))) (*.f32 (neg.f32 (PI.f32)) (PI.f32)))
(/.f32 (-.f32 (PI.f32) (.f32 (PI.f32) (.f32 #s(literal 2 binary32) cosTheta))) (*.f32 (PI.f32) (PI.f32)))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 4 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (fma.f32 #s(literal 2 binary32) cosTheta #s(literal 1 binary32))))
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(/.f32 (+.f32 (+.f32 #s(literal -1 binary32) cosTheta) cosTheta) (neg.f32 (PI.f32)))
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(-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32)))
(fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(fma.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32)) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(fma.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (PI.f32)) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(pow.f32 (/.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal -1 binary32))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (neg.f32 (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) (PI.f32))))
(exp.f32 (*.f32 (log.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal -1 binary32)))
(neg.f32 (/.f32 (+.f32 (+.f32 #s(literal -1 binary32) cosTheta) cosTheta) (PI.f32)))
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eval189.0ms (1.9%)

Memory: 5.6MiB live, 348.7MiB allocated
Compiler: Compiled 52 467 to 5 504 computations (89.5% saved)

prune71.0ms (0.7%)

Memory

2.2MiB live, 176.0MiB allocated

Pruning

33 alts after pruning (25 fresh and 8 done)

	Pruned	Kept	Total
New	1 079	17	1 096
Fresh	7	8	15
Picked	2	3	5
Done	0	5	5
Total	1 088	33	1 121

Accuracy

100.0%

Counts

1 121 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.2%	(/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
	94.5%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))) (/.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
	95.2%	(/.f32 (sqrt.f32 (PI.f32)) (*.f32 (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))))
	95.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 c #s(literal 1 binary32)) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	91.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 c c #s(literal -1 binary32))) (-.f32 c #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	94.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 c c))) (-.f32 #s(literal 1 binary32) c))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	88.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (sqrt.f32 (PI.f32)))))
	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32)))))
	88.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (-.f32 (sqrt.f32 (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) c)))))
	91.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* cosTheta c) cosTheta) (.f32 (+.f32 (/.f32 cosTheta c) cosTheta) c))))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
✓	97.8%	(/.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)))))
✓	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	94.6%	(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	91.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
✓	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	91.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	57.5%	(*.f32 (/.f32 (/.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal 2 binary32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (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)))))
	58.2%	(.f32 (/.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (-.f32 (PI.f32) (pow.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))) #s(literal 2 binary32)))) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (+.f32 c #s(literal 1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))))
	58.1%	(.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (/.f32 (-.f32 (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 (PI.f32) (pow.f32 (.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) #s(literal -2 binary32)))))
	95.2%	(*.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	95.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))) (sqrt.f32 (PI.f32)))
	95.1%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))))
	95.3%	#s(approx (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (fma.f32 cosTheta c cosTheta) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))) (sqrt.f32 (PI.f32)))) cosTheta))
	95.3%	#s(approx (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (fma.f32 c cosTheta cosTheta) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))) (sqrt.f32 (PI.f32)))) cosTheta))
	92.1%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) cosTheta)) cosTheta))
	95.4%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (PI.f32) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
	92.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
✓	92.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))

Compiler

Compiled 3 608 to 1 153 computations (68% saved)

regimes109.0ms (1.1%)

Memory

-6.1MiB live, 268.0MiB allocated

Counts

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

Calls

6 calls:

21.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
18.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
18.0ms	cosTheta
17.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
17.0ms	c

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta`
98.3%	1	`c`
98.3%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.3%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.3%	1	`(+.f32 #s(literal 1 binary32) c)`
98.3%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes102.0ms (1.1%)

Memory

7.7MiB live, 266.1MiB allocated

Counts

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

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 (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Calls

6 calls:

31.0ms	cosTheta
16.0ms	(+.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))))
15.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
13.0ms	c

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)

regimes224.0ms (2.3%)

Memory

-23.3MiB live, 171.6MiB allocated

Counts

46 → 1

Calls

Call 1

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

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)))))

Calls

6 calls:

158.0ms	cosTheta
14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
14.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
12.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
12.0ms	c

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)

regimes98.0ms (1%)

Memory

14.7MiB live, 92.3MiB allocated

Counts

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

Calls

6 calls:

35.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
22.0ms	c
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes100.0ms (1%)

Memory

-9.1MiB live, 69.9MiB allocated

Counts

37 → 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) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (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) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (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)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) cosTheta)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (PI.f32) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
(/.f32 (sqrt.f32 (PI.f32)) (*.f32 (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))))
#s(approx (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (fma.f32 c cosTheta cosTheta) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))) (sqrt.f32 (PI.f32)))) cosTheta))
#s(approx (/ 1 (/ (+ (sqrt (PI)) (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)))) (* (/ 1 (+ c 1)) (sqrt (PI))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (fma.f32 cosTheta c cosTheta) (-.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))) (sqrt.f32 (PI.f32)))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32)))) (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))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.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 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (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))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (sqrt.f32 (PI.f32)))))
(*.f32 (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))))
(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))) (/.f32 (+.f32 c #s(literal 1 binary32)) (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))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 (sqrt.f32 (PI.f32)) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)) (+.f32 c #s(literal 1 binary32)))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (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))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) #s(approx ( (/ 1 (+ c 1)) (sqrt (PI))) (-.f32 (sqrt.f32 (PI.f32)) (*.f32 (sqrt.f32 (PI.f32)) c)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* cosTheta c) cosTheta) (.f32 (+.f32 (/.f32 cosTheta c) cosTheta) c))))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (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))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (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))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) 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 (sqrt.f32 (PI.f32)) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 c c #s(literal -1 binary32))) (-.f32 c #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 c #s(literal 1 binary32)) #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) 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 (sqrt.f32 (PI.f32)) (.f32 (/.f32 #s(approx (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 c c))) (-.f32 #s(literal 1 binary32) c))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(approx (* (/ 1 (+ c 1)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (exp cosTheta) cosTheta))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) c))) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (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:

41.0ms	c
19.0ms	cosTheta
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

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

regimes66.0ms (0.7%)

Memory

32.2MiB live, 68.7MiB allocated

Counts

36 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

17.0ms	c
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	(/.f32 #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
95.4%	1	`cosTheta`
95.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.4%	1	`(+.f32 #s(literal 1 binary32) c)`
95.4%	1	`c`
95.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes28.0ms (0.3%)

Memory

-16.5MiB live, 20.8MiB 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) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (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) (cbrt (PI))) (/ 1 (pow (PI) 1/6))) (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)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (* (PI) (log (E)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) cosTheta)) cosTheta))

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:

12.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
3.0ms	c
3.0ms	cosTheta

Results

Accuracy	Segments	Branch
92.4%	1	`cosTheta`
92.4%	1	`c`
92.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
92.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
92.4%	1	`(+.f32 #s(literal 1 binary32) c)`
92.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes20.0ms (0.2%)

Memory

-25.6MiB live, 21.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

13.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
1.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
1.0ms	c
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
5.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
5.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
5.1%	1	`c`
5.1%	1	`(+.f32 #s(literal 1 binary32) c)`
5.1%	1	`cosTheta`
5.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify77.0ms (0.8%)

Memory

7.9MiB live, 44.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	223
1	123	222
2	158	222
3	223	222
4	353	222
5	553	222
6	778	222
7	1017	222
8	1210	222
9	1365	222
10	1481	222
11	1589	222
12	1660	222
13	1690	222
14	1696	222
15	1696	222

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.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)))) (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 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.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 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (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)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (PI.f32) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (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 (/.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)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (-.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))))) (-.f32 #s(literal -1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (-.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (.f32 (log.f32 (E.f32)) (PI.f32))) cosTheta)) (exp.f32 (.f32 (neg.f32 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 #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 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) 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 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta))) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (-.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 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(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)))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (PI.f32) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 (PI.f32) cosTheta))) 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))

soundness773.0ms (8%)

Memory

-5.2MiB live, 356.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	440
0	107	423
1	441	408
2	3755	408
0	8364	403
0	1546	18881
1	5154	17675
0	8221	17135
0	59	389
0	98	408
1	410	346
2	3316	346
0	8641	339
0	407	3010
1	1237	2916
2	4721	2838
0	8274	2706
0	18	73
0	33	73
1	141	66
2	1060	61
0	8551	61

Stop Event

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

Compiler

Compiled 644 to 324 computations (49.7% saved)

preprocess59.0ms (0.6%)

Memory: 20.0MiB live, 58.4MiB allocated
Compiler: Compiled 494 to 204 computations (58.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze32.0ms (0.3%)

sample2.1s (21.8%)

explain362.0ms (3.7%)

preprocess251.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify137.0ms (1.4%)

localize99.0ms (1%)

series28.0ms (0.3%)

simplify293.0ms (3%)

rewrite153.0ms (1.6%)

eval73.0ms (0.7%)

prune25.0ms (0.3%)

simplify121.0ms (1.2%)

localize216.0ms (2.2%)

series260.0ms (2.7%)

simplify304.0ms (3.1%)

rewrite270.0ms (2.8%)

eval251.0ms (2.6%)

prune49.0ms (0.5%)

simplify153.0ms (1.6%)

localize401.0ms (4.1%)

series146.0ms (1.5%)

simplify264.0ms (2.7%)

rewrite231.0ms (2.4%)

eval274.0ms (2.8%)

prune47.0ms (0.5%)

simplify113.0ms (1.2%)

localize385.0ms (4%)

series177.0ms (1.8%)

simplify262.0ms (2.7%)

rewrite302.0ms (3.1%)

eval189.0ms (1.9%)

prune71.0ms (0.7%)

regimes109.0ms (1.1%)

regimes102.0ms (1.1%)

regimes224.0ms (2.3%)

regimes98.0ms (1%)

regimes100.0ms (1%)

regimes66.0ms (0.7%)

regimes28.0ms (0.3%)

regimes20.0ms (0.2%)

simplify77.0ms (0.8%)

soundness773.0ms (8%)

preprocess59.0ms (0.6%)

end0.0ms (0%)

Profiling