Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze50.0ms (0.6%)

Memory

-9.4MiB live, 71.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.1s (23.7%)

Memory

-74.4MiB live, 2 399.6MiB allocated

Samples

1.7s	8 256×	0	valid
10.0ms	72×	0	invalid

Precisions

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

ival-sub: 211.0ms (16.4% of total)

ival-mult: 204.0ms (15.9% of total)

ival-div: 189.0ms (14.7% of total)

const: 156.0ms (12.1% of total)

ival-sqrt: 156.0ms (12.1% of total)

ival-<: 101.0ms (7.9% of total)

ival-add: 88.0ms (6.8% of total)

ival-exp: 67.0ms (5.2% of total)

ival-neg: 42.0ms (3.3% of total)

ival-pi: 30.0ms (2.3% of total)

ival-and: 23.0ms (1.8% of total)

exact: 14.0ms (1.1% of total)

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

Bogosity

explain225.0ms (2.5%)

Memory

20.4MiB live, 289.4MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

61.0ms

512×

valid

Compiler

Compiled 407 to 76 computations (81.3% saved)

Precisions

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

ival-div: 9.0ms (20.9% of total)

ival-mult: 9.0ms (20.9% of total)

ival-sqrt: 7.0ms (16.2% of total)

ival-add: 5.0ms (11.6% of total)

ival-exp: 4.0ms (9.3% of total)

ival-sub: 4.0ms (9.3% of total)

ival-pi: 2.0ms (4.6% of total)

ival-neg: 2.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess205.0ms (2.3%)

Memory

8.9MiB live, 122.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	127
1	135	117
2	394	111
3	1325	110
4	3721	110
5	5376	110
6	7089	110
7	7837	110
0	18	25
0	33	25
1	59	23
2	122	22
3	242	22
4	366	22
5	743	22
6	1896	22
7	2875	22
8	3432	22
9	4062	22
10	4230	22
11	4263	22
12	4296	22
13	4430	22
14	5055	22
15	5063	22
16	5067	22
17	5067	22
0	5067	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: 0.2MiB live, 0.2MiB 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
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

97.9%

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

Compiler

Compiled 25 to 18 computations (28% saved)

simplify155.0ms (1.7%)

Memory

1.5MiB live, 112.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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	1	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff	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)))
cost-diff	2	(*.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	366	115
5	743	115
6	1896	115
7	2875	115
8	3432	115
9	4062	115
10	4230	115
11	4263	115
12	4296	115
13	4430	115
14	5055	115
15	5063	115
16	5067	115
17	5067	115
0	5067	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)

localize71.0ms (0.8%)

Memory

-14.1MiB live, 111.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.2734375	(/.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	0.6097450683790941	(*.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

37.0ms

256×

valid

Compiler

Compiled 254 to 38 computations (85% saved)

Precisions

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

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

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

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

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.3%)

Memory

14.1MiB live, 51.6MiB allocated

Counts

5 → 50

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	cosTheta	@	inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
8.0ms	cosTheta	@	-inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
2.0ms	cosTheta	@	0	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
1.0ms	c	@	0	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
1.0ms	c	@	inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))

simplify192.0ms (2.1%)

Memory

1.8MiB live, 228.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	378	2860
1	1142	2768
2	4413	2687
0	8087	2569

Stop Event

1×	iter limit
1×	node limit

Counts

50 → 50

Calls

Call 1

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

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

rewrite234.0ms (2.6%)

Memory

-0.1MiB live, 247.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	66
0	33	66
1	141	59
2	1060	54
0	8671	54

Stop Event

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

Counts

5 → 354

Calls

Call 1

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

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

eval82.0ms (0.9%)

Memory: -17.7MiB live, 154.8MiB allocated
Compiler: Compiled 16 617 to 2 452 computations (85.2% saved)

prune55.0ms (0.6%)

Memory

-17.2MiB live, 60.8MiB allocated

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	376	24	400
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	377	24	401

Accuracy

99.8%

Counts

401 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.7%	(/.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))))
▶	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)))))
	98.4%	(/.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)))))
	98.3%	(/.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)))))
▶	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.6%	(/.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)))))
	98.7%	(/.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)))))
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	92.9%	(/.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)))))
	33.6%	(-.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)))))
	54.6%	(-.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)))))
	54.5%	(+.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 (/.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))))))
	54.6%	(*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)))
▶	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) cosTheta))
	93.6%	#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 1 652 to 954 computations (42.3% saved)

simplify176.0ms (2%)

Memory

21.1MiB live, 173.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f32 c #s(literal 1 binary32))
cost-diff	0	(-.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))
cost-diff	1	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff	21	(/.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))))
cost-diff	1	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff	1	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff	2	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta))
cost-diff	4	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	1	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff	1	(.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff	0	(/.f32 #s(literal 1 binary32) c)
cost-diff	0	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
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)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
cost-diff	1	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	584
0	100	542
1	178	540
2	335	539
3	732	539
4	2002	517
5	7400	517
0	8822	486

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

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

localize254.0ms (2.8%)

Memory

17.4MiB live, 219.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.23046875	(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))
accuracy	0.63671875	(/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)
accuracy	0.80859375	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	14.430798642356928	(/.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))))
accuracy	0.11714015715245243	(PI.f32)
accuracy	0.26953125	(/.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.6097450683790941	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta))
accuracy	0.99609375	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
accuracy	0.11714015715245243	(PI.f32)
accuracy	0.26953125	(/.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)))))
accuracy	0.28515625	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.33203125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.0	(/.f32 #s(literal 1 binary32) c)
accuracy	30.284769037229495	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy	0.11714015715245243	(PI.f32)
accuracy	0.26953125	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
accuracy	0.28515625	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.33203125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Samples

169.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 1 166 to 112 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-mult: 52.0ms (40.4% of total)

ival-div: 41.0ms (31.9% of total)

ival-sqrt: 7.0ms (5.4% of total)

ival-add: 7.0ms (5.4% of total)

ival-pow: 6.0ms (4.7% of total)

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

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

ival-pow2: 4.0ms (3.1% of total)

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

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series100.0ms (1.1%)

Memory

10.8MiB live, 117.2MiB allocated

Counts

24 → 160

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
34.0ms	c	@	0	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* cosTheta (sqrt (PI))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))
20.0ms	cosTheta	@	0	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* cosTheta (sqrt (PI))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))
13.0ms	cosTheta	@	inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* cosTheta (sqrt (PI))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))
11.0ms	cosTheta	@	-inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* cosTheta (sqrt (PI))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))
7.0ms	c	@	inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* cosTheta (sqrt (PI))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (/ 1 (/ 1 (- (- 1 cosTheta) cosTheta)))) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))

simplify355.0ms (4%)

Memory

-14.2MiB live, 233.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	985	10688
1	3135	10275
0	8363	9956

Stop Event

1×	iter limit
1×	node limit

Counts

160 → 159

Calls

Call 1

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

rewrite316.0ms (3.5%)

Memory

-7.8MiB live, 340.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	60	362
0	100	315
1	442	298
2	3764	298
0	8244	298

Stop Event

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

Counts

24 → 1 482

Calls

Call 1

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

Outputs
(.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (.f32 cosTheta cosTheta))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(*.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(.f32 (pow.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)))
(*.f32 (pow.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) #s(literal 1 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))) #s(literal 1 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) (pow.f32 (sqrt.f32 (-.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)) (.f32 cosTheta cosTheta)) (/.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 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(*.f32 #s(literal -1 binary32) (pow.f32 (neg.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)))
(*.f32 #s(literal -1 binary32) (neg.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(*.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(*.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (*.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 2 binary32))) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) (neg.f32 cosTheta)))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 8 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (+.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32)) (.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)))))
(/.f32 (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32))) (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (-.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 2 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (neg.f32 cosTheta)))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) (neg.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (.f32 cosTheta cosTheta)) (.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (*.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))))
(/.f32 (neg.f32 (-.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 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(-.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 0 binary32)) cosTheta)
(-.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (*.f32 cosTheta cosTheta) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(-.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))) (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 cosTheta #s(literal 1 binary32)))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))
(-.f32 #s(literal 1 binary32) (/.f32 (*.f32 #s(literal 2 binary32) cosTheta) #s(literal 1 binary32)))
(-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta))
(fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta))
(fma.f32 (-.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 cosTheta cosTheta cosTheta) #s(literal 1 binary32))) (neg.f32 cosTheta))
(fma.f32 #s(literal -1 binary32) cosTheta (-.f32 #s(literal 1 binary32) cosTheta))
(fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(fma.f32 cosTheta (log.f32 (exp.f32 #s(literal -1 binary32))) (-.f32 #s(literal 1 binary32) cosTheta))
(fma.f32 cosTheta #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))
(fma.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(pow.f32 (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal -1/2 binary32))
(pow.f32 (*.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1/2 binary32))
(pow.f32 (/.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) #s(literal -1 binary32))
(pow.f32 (pow.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal -1/2 binary32)) #s(literal -2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal -1 binary32))
(pow.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 2 binary32))
(pow.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal 1 binary32))
(+.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(+.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 #s(literal 1 binary32) (neg.f32 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 (neg.f32 cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (fma.f32 #s(literal -1 binary32) cosTheta (neg.f32 cosTheta)))
(+.f32 #s(literal 1 binary32) (neg.f32 (*.f32 #s(literal 2 binary32) cosTheta)))
(exp.f32 (fma.f32 (log1p.f32 (-.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 1/2 binary32) (*.f32 (log1p.f32 (-.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 1/2 binary32))))
(exp.f32 (*.f32 (log1p.f32 (-.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 1 binary32)))
(exp.f32 (log1p.f32 (-.f32 (neg.f32 cosTheta) cosTheta)))
(neg.f32 (neg.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(.f32 (pow.f32 (/.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 3 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.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 (/.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (/.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 4 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 4 binary32)))) (+.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))))
(.f32 (/.f32 (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 6 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 6 binary32)))) (+.f32 (+.f32 (pow.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 4 binary32))) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 4 binary32))))
(.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)))
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(/.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal -2 binary32)) (pow.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal 2 binary32)))
(/.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))) (.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))) (.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (pow.f32 (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 2 binary32)))
(/.f32 (.f32 (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (neg.f32 cosTheta) cosTheta))
(/.f32 (.f32 (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (.f32 (neg.f32 cosTheta) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))
(/.f32 (.f32 (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (neg.f32 cosTheta) (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (neg.f32 cosTheta) cosTheta))
(/.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (.f32 cosTheta (*.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)) #s(literal 1 binary32)) (.f32 cosTheta (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (neg.f32 cosTheta)))
(/.f32 (.f32 (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))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) cosTheta))
(/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1 binary32)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (neg.f32 cosTheta)))
(/.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) #s(literal -2 binary32)) (*.f32 cosTheta cosTheta))
(/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta))
(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)))
(/.f32 #s(literal 1 binary32) (pow.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)))
(pow.f32 (exp.f32 #s(literal 2 binary32)) (log.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))))
(pow.f32 (pow.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) #s(literal -1 binary32))
(pow.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal -2 binary32))
(pow.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)) #s(literal 1 binary32))
(pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32))
(exp.f32 (.f32 (log.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32))) #s(literal 1 binary32)))
(exp.f32 (log.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32))))

eval260.0ms (2.9%)

Memory: -4.0MiB live, 423.8MiB allocated
Compiler: Compiled 68 633 to 6 747 computations (90.2% saved)

prune106.0ms (1.2%)

Memory

-25.1MiB live, 134.1MiB allocated

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	1 456	15	1 471
Fresh	11	8	19
Picked	3	2	5
Done	0	0	0
Total	1 470	25	1 495

Accuracy

99.9%

Counts

1 495 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	54.1%	(/.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)) (/.f32 (pow.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)) (PI.f32))))
▶	48.6%	(/.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)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))))
	52.2%	(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (-.f32 (*.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 (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))))
	54.0%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
▶	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))
	98.4%	(/.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)))))
	98.3%	(/.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)))))
	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.4%	(/.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 (.f32 (PI.f32) (log.f32 (E.f32)))))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
	98.1%	(/.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)))))
▶	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	93.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	54.6%	(-.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))))
	54.5%	(+.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 (/.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))))))
	54.6%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))))
▶	93.6%	#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) cosTheta))

Compiler

Compiled 1 614 to 998 computations (38.2% saved)

simplify166.0ms (1.8%)

Memory

11.5MiB live, 179.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	651
0	116	642
1	194	632
2	366	632
3	723	629
4	1420	629
5	4683	629
0	8132	601

Stop Event

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

Calls

Call 1

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

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

localize171.0ms (1.9%)

Memory

-2.7MiB live, 309.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.63671875	(/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) cosTheta)
accuracy	0.8125	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	2.038767151270143	#s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
accuracy	14.434704892356928	(/.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)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))))
accuracy	0.10546875	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.26171875	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)))
accuracy	0.2734375	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.4140625	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
accuracy	0.2734375	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.640625	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
accuracy	0.6827632211362312	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	0.0	(sqrt.f32 (PI.f32))
accuracy	0.0	(PI.f32)
accuracy	0.33203125	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	1.7545685280031995	#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.10546875	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.2734375	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))
accuracy	0.28515625	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (sqrt.f32 (PI.f32))))
accuracy	0.33203125	(.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))

Samples

123.0ms

256×

valid

Compiler

Compiled 1 231 to 128 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-div: 34.0ms (35.8% of total)

ival-mult: 19.0ms (20% of total)

ival-sqrt: 14.0ms (14.8% of total)

ival-add: 7.0ms (7.4% of total)

ival-pow: 6.0ms (6.3% of total)

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

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

ival-pow2: 4.0ms (4.2% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series33.0ms (0.4%)

Memory

22.5MiB live, 60.1MiB allocated

Counts

26 → 177

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	cosTheta	@	-inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta))
5.0ms	c	@	0	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta))
5.0ms	cosTheta	@	inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta))
4.0ms	cosTheta	@	0	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta))
3.0ms	c	@	inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ 1 (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))) (exp (* (neg cosTheta) cosTheta))))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (+ c 1) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta) (/ (sqrt (PI)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta))

simplify236.0ms (2.6%)

Memory

-6.4MiB live, 306.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1096	11132
1	3542	10681
0	8594	10348

Stop Event

1×	iter limit
1×	node limit

Counts

177 → 176

Calls

Call 1

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

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

rewrite271.0ms (3%)

Memory

10.9MiB live, 245.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	436
0	116	431
1	460	393
2	4501	393
0	8171	391

Stop Event

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

Counts

26 → 1 122

Calls

Call 1

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

Outputs
(.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(*.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 2 binary32))) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) (neg.f32 cosTheta)))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 8 binary32) (pow.f32 cosTheta #s(literal 3 binary32)))) (+.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (.f32 #s(literal 2 binary32) cosTheta) #s(literal 2 binary32)) (.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)))))
(/.f32 (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32))) (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (-.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 2 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (neg.f32 cosTheta)))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) (neg.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
(/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32))) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))))
(-.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 0 binary32)) cosTheta)
(-.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (*.f32 cosTheta cosTheta) (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(-.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))) (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)))))
(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))
(-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta))
(fma.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta))
(fma.f32 (-.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 cosTheta cosTheta cosTheta) #s(literal 1 binary32))) (neg.f32 cosTheta))
(fma.f32 #s(literal -1 binary32) cosTheta (-.f32 #s(literal 1 binary32) cosTheta))
(fma.f32 cosTheta (log.f32 (exp.f32 #s(literal -1 binary32))) (-.f32 #s(literal 1 binary32) cosTheta))
(fma.f32 cosTheta #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))
(pow.f32 (/.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 3 binary32)) (pow.f32 cosTheta #s(literal 3 binary32)))) #s(literal -1 binary32))
(+.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 (neg.f32 cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (fma.f32 #s(literal -1 binary32) cosTheta (neg.f32 cosTheta)))
(+.f32 #s(literal 1 binary32) (neg.f32 (*.f32 #s(literal 2 binary32) cosTheta)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)))
(*.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))))))
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32)))) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (exp.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c))) #s(literal -1 binary32))
(pow.f32 (*.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.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 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32)))) #s(literal -1/2 binary32))
(pow.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))))) #s(literal -1 binary32))
(pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(.f32 (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))))
(.f32 (+.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.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 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal 1 binary32))
(/.f32 (-.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)) (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) 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 (neg.f32 cosTheta)) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c)))
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(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))
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(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.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) (/.f32 (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta)))
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(pow.f32 (.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal -1 binary32))
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(exp.f32 (.f32 (log.f32 (.f32 (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (pow.f32 (exp.f32 cosTheta) cosTheta))) #s(literal -1 binary32)))
(exp.f32 (log.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))))
(neg.f32 (/.f32 (/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(neg.f32 (/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(neg.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(neg.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (neg.f32 (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(neg.f32 (/.f32 (neg.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)))

eval254.0ms (2.8%)

Memory: 1.9MiB live, 403.1MiB allocated
Compiler: Compiled 67 290 to 6 620 computations (90.2% saved)

prune45.0ms (0.5%)

Memory

-13.4MiB live, 111.6MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	1 417	10	1 427
Fresh	6	12	18
Picked	4	1	5
Done	0	2	2
Total	1 427	25	1 452

Accuracy

100.0%

Counts

1 452 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.8%	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	29.2%	(/.f32 (/.f32 (-.f32 (.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) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))))
	54.1%	(/.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)) (/.f32 (pow.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)) (PI.f32))))
	52.2%	(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (-.f32 (*.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 (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))))
▶	49.5%	(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))))
	53.0%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
▶	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))))
	96.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)))))
	98.4%	(/.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)))))
	98.3%	(/.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)))))
	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	93.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	54.6%	(-.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))))
	54.5%	(+.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 (/.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))))))
	52.7%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
✓	93.6%	#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) cosTheta))

Compiler

Compiled 1 797 to 1 084 computations (39.7% saved)

simplify172.0ms (1.9%)

Memory

-2.5MiB live, 153.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	636
0	115	636
1	189	626
2	329	626
3	572	623
4	992	623
5	2714	623
6	5827	623
0	8595	600

Stop Event

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

Calls

Call 1

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

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

localize217.0ms (2.4%)

Memory

-14.6MiB live, 311.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32))
accuracy	0.5397262695368841	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
accuracy	0.62890625	(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta))
accuracy	0.8125	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	2.038767151270143	#s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
accuracy	2.119024104460059	#s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta)))
accuracy	14.434704892356928	(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))))
accuracy	0.2734375	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.640625	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)
accuracy	0.6827632211362312	#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
accuracy	0.82421875	(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	0.2734375	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
accuracy	0.69140625	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	1.7483224824702326	#s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
accuracy	0.10546875	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.2734375	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))))
accuracy	0.28515625	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
accuracy	0.32421875	(.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)

Samples

127.0ms

256×

valid

Compiler

Compiled 1 184 to 131 computations (88.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-div: 33.0ms (37.5% of total)

ival-mult: 13.0ms (14.8% of total)

ival-pow: 10.0ms (11.4% of total)

ival-add: 7.0ms (8% of total)

ival-sqrt: 7.0ms (8% of total)

ival-pow2: 7.0ms (8% of total)

ival-exp: 4.0ms (4.5% of total)

ival-sub: 4.0ms (4.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series78.0ms (0.9%)

Memory

6.6MiB live, 79.6MiB allocated

Counts

25 → 193

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	cosTheta	@	-inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/ (sqrt (/ 1 (PI))) (neg cosTheta)) (pow (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) 2) (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)) (/ (- 1 cosTheta) (sqrt (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (/ (- 1 cosTheta) (sqrt (PI))) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)))
8.0ms	cosTheta	@	inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/ (sqrt (/ 1 (PI))) (neg cosTheta)) (pow (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) 2) (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)) (/ (- 1 cosTheta) (sqrt (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (/ (- 1 cosTheta) (sqrt (PI))) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)))
4.0ms	cosTheta	@	0	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/ (sqrt (/ 1 (PI))) (neg cosTheta)) (pow (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) 2) (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)) (/ (- 1 cosTheta) (sqrt (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (/ (- 1 cosTheta) (sqrt (PI))) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)))
4.0ms	c	@	0	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/ (sqrt (/ 1 (PI))) (neg cosTheta)) (pow (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) 2) (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)) (/ (- 1 cosTheta) (sqrt (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (/ (- 1 cosTheta) (sqrt (PI))) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)))
4.0ms	c	@	-inf	((- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta))) (+ 1 c) (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (- (pow (+ c 1) 2) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2))) (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/ (sqrt (/ 1 (PI))) (neg cosTheta)) (pow (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) 2) (pow (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) -1/2) (+ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)) (+ c 1)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)) (/ (- 1 cosTheta) (sqrt (PI))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (/ (- 1 cosTheta) (sqrt (PI))) cosTheta) (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (* (pow (exp cosTheta) cosTheta) cosTheta)))

simplify199.0ms (2.2%)

Memory

14.8MiB live, 327.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1170	13693
1	3728	12985
0	8141	12579

Stop Event

1×	iter limit
1×	node limit

Counts

193 → 192

Calls

Call 1

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

rewrite340.0ms (3.8%)

Memory

8.6MiB live, 252.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	475
0	115	476
1	480	445
2	4691	445
0	8299	443

Stop Event

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

Counts

25 → 992

Calls

Call 1

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

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

eval142.0ms (1.6%)

Memory: 28.2MiB live, 218.2MiB allocated
Compiler: Compiled 48 755 to 4 541 computations (90.7% saved)

prune49.0ms (0.5%)

Memory

-26.1MiB live, 132.9MiB allocated

Pruning

29 alts after pruning (22 fresh and 7 done)

	Pruned	Kept	Total
New	980	8	988
Fresh	3	14	17
Picked	1	4	5
Done	0	3	3
Total	984	29	1 013

Accuracy

100.0%

Counts

1 013 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.8%	(pow.f32 (pow.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	29.3%	(/.f32 (/.f32 (-.f32 (.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) cosTheta)))) (.f32 (-.f32 c #s(literal 1 binary32)) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))))
	54.1%	(/.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)) (/.f32 (pow.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)) (PI.f32))))
	52.2%	(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (-.f32 (*.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 (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))))
	49.5%	(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal -1 binary32) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
✓	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))))
	96.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)))))
	98.4%	(/.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)))))
	98.3%	(/.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)))))
	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	93.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
✓	93.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	93.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	54.6%	(-.f32 (/.f32 (+.f32 c #s(literal 1 binary32)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (*.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta)) #s(literal 2 binary32)))))
	54.5%	(+.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 (/.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))))))
	52.7%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) #s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta))) #s(literal 2 binary32)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))) cosTheta))
✓	93.6%	#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	93.6%	#s(approx (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (*.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))
✓	5.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) cosTheta))

Compiler

Compiled 3 133 to 1 012 computations (67.7% saved)

regimes106.0ms (1.2%)

Memory

11.6MiB live, 244.9MiB allocated

Counts

58 → 1

Calls

Call 1

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

Calls

6 calls:

20.0ms	(+.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))))
19.0ms	c
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)))
17.0ms	cosTheta
15.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.8%	1	`cosTheta`
98.8%	1	`c`
98.8%	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)))))`
98.8%	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))))`
98.8%	1	`(+.f32 #s(literal 1 binary32) c)`
98.8%	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)

regimes109.0ms (1.2%)

Memory

4.0MiB live, 100.0MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

48.0ms	c
17.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
11.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
11.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
11.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.8%	1	`cosTheta`
98.8%	1	`c`
98.8%	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)))))`
98.8%	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))))`
98.8%	1	`(+.f32 #s(literal 1 binary32) c)`
98.8%	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)

regimes73.0ms (0.8%)

Memory

-26.0MiB live, 132.0MiB 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)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (*.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))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (.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 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal -1 binary32) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))))
(/.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 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 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) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) cosTheta) (sqrt.f32 (PI.f32))))))

Outputs

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

Calls

6 calls:

14.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
12.0ms	(+.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))))
11.0ms	cosTheta
11.0ms	c

Results

Accuracy	Segments	Branch
98.8%	1	`cosTheta`
98.8%	1	`c`
98.8%	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)))))`
98.8%	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))))`
98.8%	1	`(+.f32 #s(literal 1 binary32) c)`
98.8%	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)

regimes121.0ms (1.3%)

Memory

9.9MiB live, 87.5MiB 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)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI))))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta)))) (*.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))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (* (* (pow (exp cosTheta) cosTheta) cosTheta) (sqrt (PI))) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (* (* (pow (exp cosTheta) cosTheta) (sqrt (PI))) cosTheta) (.f32 (.f32 (fma.f32 cosTheta cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))) (.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 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal -1 binary32) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))))
(/.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 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (-.f32 cosTheta (neg.f32 cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(approx (- (+ c 1) (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))) (-.f32 (pow.f32 (+.f32 c #s(literal 1 binary32)) #s(literal 2 binary32)) #s(approx (pow (/ (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (pow (exp cosTheta) cosTheta)) cosTheta) 2) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 c #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 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) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (-.f32 (-.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) 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:

50.0ms	(+.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))))
30.0ms	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
98.8%	1	`c`
98.8%	1	`cosTheta`
98.8%	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)))))`
98.8%	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))))`
98.8%	1	`(+.f32 #s(literal 1 binary32) c)`
98.8%	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)

regimes43.0ms (0.5%)

Memory

18.3MiB live, 59.7MiB allocated

Counts

21 → 1

Calls

Call 1

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

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:

11.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
6.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
6.0ms	c
6.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes46.0ms (0.5%)

Memory

-12.5MiB live, 62.0MiB allocated

Counts

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

Outputs

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

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)))
12.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
6.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
6.0ms	c
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.8%	1	`cosTheta`
96.8%	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)))))`
96.8%	1	`c`
96.8%	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))))`
96.8%	1	`(+.f32 #s(literal 1 binary32) c)`
96.8%	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)

regimes32.0ms (0.4%)

Memory

5.6MiB live, 44.4MiB allocated

Counts

11 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	c
4.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes28.0ms (0.3%)

Memory

-8.9MiB live, 37.1MiB allocated

Counts

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

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:

13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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
93.6%	1	`cosTheta`
93.6%	1	`c`
93.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
93.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
93.6%	1	`(+.f32 #s(literal 1 binary32) c)`
93.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes8.0ms (0.1%)

Memory

19.5MiB live, 19.5MiB 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:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify57.0ms (0.6%)

Memory

-17.3MiB live, 58.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	236
1	120	230
2	195	228
3	323	228
4	451	228
5	1042	228
6	5304	228

Stop Event

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

soundness929.0ms (10.3%)

Memory

2.6MiB live, 330.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	2860
1	1142	2768
2	4413	2687
0	8087	2569
0	60	362
0	100	315
1	442	298
2	3764	298
0	8244	298
0	1096	11132
1	3542	10681
0	8594	10348
0	70	436
0	116	431
1	460	393
2	4501	393
0	8171	391
0	71	475
0	115	476
1	480	445
2	4691	445
0	8299	443
0	18	66
0	33	66
1	141	59
2	1060	54
0	8671	54

Stop Event

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

Compiler

Compiled 690 to 352 computations (49% saved)

preprocess73.0ms (0.8%)

Memory: -5.0MiB live, 34.0MiB allocated
Compiler: Compiled 522 to 186 computations (64.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze50.0ms (0.6%)

sample2.1s (23.7%)

explain225.0ms (2.5%)

preprocess205.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify155.0ms (1.7%)

localize71.0ms (0.8%)

series26.0ms (0.3%)

simplify192.0ms (2.1%)

rewrite234.0ms (2.6%)

eval82.0ms (0.9%)

prune55.0ms (0.6%)

simplify176.0ms (2%)

localize254.0ms (2.8%)

series100.0ms (1.1%)

simplify355.0ms (4%)

rewrite316.0ms (3.5%)

eval260.0ms (2.9%)

prune106.0ms (1.2%)

simplify166.0ms (1.8%)

localize171.0ms (1.9%)

series33.0ms (0.4%)

simplify236.0ms (2.6%)

rewrite271.0ms (3%)

eval254.0ms (2.8%)

prune45.0ms (0.5%)

simplify172.0ms (1.9%)

localize217.0ms (2.4%)

series78.0ms (0.9%)

simplify199.0ms (2.2%)

rewrite340.0ms (3.8%)

eval142.0ms (1.6%)

prune49.0ms (0.5%)

regimes106.0ms (1.2%)

regimes109.0ms (1.2%)

regimes73.0ms (0.8%)

regimes121.0ms (1.3%)

regimes43.0ms (0.5%)

regimes46.0ms (0.5%)

regimes32.0ms (0.4%)

regimes28.0ms (0.3%)

regimes8.0ms (0.1%)

simplify57.0ms (0.6%)

soundness929.0ms (10.3%)

preprocess73.0ms (0.8%)

end0.0ms (0%)

Profiling