Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze58.0ms (0.6%)

Memory

-12.2MiB live, 52.0MiB allocated; 37ms collecting garbage

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)

sample2.0s (21.8%)

Memory

43.2MiB live, 2 394.3MiB allocated; 554ms collecting garbage

Samples

1.4s	8 256×	0	valid
9.0ms	67×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

const: 248.0ms (20.2% of total)

ival-mult: 217.0ms (17.7% of total)

ival-div: 193.0ms (15.7% of total)

ival-sqrt: 115.0ms (9.4% of total)

ival-add: 108.0ms (8.8% of total)

ival-<: 85.0ms (6.9% of total)

ival-sub: 81.0ms (6.6% of total)

ival-exp: 65.0ms (5.3% of total)

ival-pi: 35.0ms (2.9% of total)

ival-neg: 35.0ms (2.9% of total)

ival-and: 24.0ms (2% of total)

exact: 14.0ms (1.1% of total)

adjust: 3.0ms (0.2% of total)

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

Bogosity

explain231.0ms (2.6%)

Memory

6.5MiB live, 398.2MiB allocated; 43ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.48552361130714417 5.2398538635246736e-33)	`(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)`
0	-	0	-	`(sqrt.f32 (PI.f32))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(*.f32 (neg.f32 cosTheta) cosTheta)`
0	-	0	-	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`
0	-	0	-	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
0	-	0	-	`(+.f32 #s(literal 1 binary32) c)`
0	-	0	-	`cosTheta`
0	-	0	-	`(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))`
0	-	0	-	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
0	-	0	-	`c`
0	-	0	-	`(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))`
0	-	0	-	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
0	-	0	-	`(-.f32 #s(literal 1 binary32) cosTheta)`
0	-	0	-	`#s(literal 1 binary32)`
0	-	0	-	`(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)`
0	-	0	-	`(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))`
0	-	0	-	`(neg.f32 cosTheta)`

Confusion

	Predicted +	Predicted -
+	0	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

66.0ms

512×

valid

Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-div: 11.0ms (24.1% of total)

ival-mult: 9.0ms (19.7% of total)

ival-sqrt: 6.0ms (13.1% of total)

ival-add: 5.0ms (10.9% of total)

ival-sub: 5.0ms (10.9% of total)

ival-exp: 4.0ms (8.8% of total)

ival-neg: 3.0ms (6.6% of total)

ival-pi: 2.0ms (4.4% of total)

ival-true: 1.0ms (2.2% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

preprocess162.0ms (1.8%)

Memory

10.8MiB live, 197.0MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	133
1	138	119
2	473	112
3	2127	110
0	18	25
0	33	25
1	60	23
2	173	22
3	742	22
4	3742	22
0	8784	21

Stop Event

1×	iter limit
1×	node limit
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) (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 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 c #s(literal -1 binary32))))

Compiler

Compiled 25 to 18 computations (28% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

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)

simplify129.0ms (1.4%)

Memory

-7.6MiB live, 179.7MiB allocated; 16ms collecting garbage

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	60	118
2	173	115
3	742	115
4	3742	115
0	8784	108

Stop Event

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

Calls

Call 1

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

localize61.0ms (0.7%)

Memory

29.2MiB live, 116.3MiB allocated; 12ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.11362290172363414	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.265625	(/.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	0.6113663086106522	(*.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

49.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-div: 15.0ms (38.3% of total)

ival-add: 9.0ms (23% of total)

ival-mult: 5.0ms (12.8% of total)

ival-sqrt: 3.0ms (7.7% of total)

ival-exp: 2.0ms (5.1% of total)

ival-sub: 2.0ms (5.1% of total)

ival-pi: 1.0ms (2.6% of total)

ival-neg: 1.0ms (2.6% 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)

series34.0ms (0.4%)

Memory

-25.0MiB live, 55.1MiB allocated; 20ms collecting garbage

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
10.0ms	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))))
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))))
6.0ms	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))))
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))))

simplify294.0ms (3.3%)

Memory

28.1MiB live, 327.5MiB allocated; 142ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	378	2856
1	1220	2772
2	5849	2705
0	8690	2591

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

rewrite72.0ms (0.8%)

Memory

-30.6MiB live, 105.6MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	66
0	33	66
1	133	59
0	1016	58

Stop Event

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

Counts

5 → 69

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

eval21.0ms (0.2%)

Memory: -7.9MiB live, 51.2MiB allocated; 9ms collecting garbage
Compiler: Compiled 5 885 to 830 computations (85.9% saved)

prune17.0ms (0.2%)

Memory

39.8MiB live, 39.8MiB allocated; 0ms collecting garbage

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	95	24	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	24	120

Accuracy

99.7%

Counts

120 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))))
	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (cosh.f32 (.f32 cosTheta cosTheta)) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))))
	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32)))))
▶	98.7%	(/.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 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.5%	(/.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)))))
▶	98.7%	(/.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)))))
	98.0%	(/.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) (.f32 (.f32 #s(literal 2 binary32) cosTheta) (.f32 #s(literal 2 binary32) cosTheta))) (+.f32 #s(literal 1 binary32) (.f32 #s(literal 2 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 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) 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 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	91.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	94.6%	(/.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 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 #s(approx ( (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (fma.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	98.1%	(*.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
	58.9%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))))))
	37.2%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 3 binary32)) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 3 binary32)))) (fma.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))) (-.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))) (-.f32 c #s(literal -1 binary32))) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32))))
	90.6%	(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) c)) #s(literal -1 binary32)))
	97.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.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))))
▶	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))
▶	96.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	94.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) 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))
	92.3%	#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 1 748 to 1 108 computations (36.6% saved)

simplify145.0ms (1.6%)

Memory

-13.6MiB live, 173.9MiB allocated; 40ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32)))
cost-diff	0	(.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
cost-diff	0	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
cost-diff	2	(.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (PI.f32)))))
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	1	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) 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 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 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 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) 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 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
cost-diff	1	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
cost-diff	1	(*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	766
0	122	766
1	223	754
2	639	737
3	2481	737
0	8142	711

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

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

localize231.0ms (2.6%)

Memory

-16.6MiB live, 413.1MiB allocated; 115ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.98828125	(pow.f32 (PI.f32) #s(literal 3 binary32))
accuracy	0.98828125	(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32)))
accuracy	0.98828125	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	1.0010817884818226	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
accuracy	0.26171875	(/.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 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.35142047145735733	(PI.f32)
accuracy	0.6035538086106522	(.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta))
accuracy	0.98828125	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
accuracy	0.23828125	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.26171875	(/.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	0.30078125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.35142047145735733	(PI.f32)
accuracy	0.0	(/.f32 #s(literal 1 binary32) c)
accuracy	30.040885050387388	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy	0.25390625	(/.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.26171875	(/.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 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
accuracy	0.30078125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.35142047145735733	(PI.f32)

Samples

120.0ms	253×	0	valid
50.0ms	3×	5	exit

Compiler

Compiled 675 to 57 computations (91.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 146.0ms

adjust: 47.0ms (32.2% of total)

ival-mult: 25.0ms (17.1% of total)

ival-div: 15.0ms (10.3% of total)

ival-add: 14.0ms (9.6% of total)

ival-pow: 11.0ms (7.5% of total)

ival-sqrt: 10.0ms (6.8% of total)

ival-neg: 8.0ms (5.5% of total)

ival-sub: 7.0ms (4.8% of total)

ival-exp: 5.0ms (3.4% of total)

ival-pow2: 2.0ms (1.4% of total)

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

exact: 1.0ms (0.7% of total)

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

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

series57.0ms (0.6%)

Memory

16.0MiB live, 107.2MiB allocated; 13ms collecting garbage

Counts

26 → 120

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	cosTheta	@	inf	((* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ 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 (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))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (PI) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (- (+ 1 c) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))) (pow (PI) 3))
13.0ms	c	@	0	((* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ 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 (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))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (PI) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (- (+ 1 c) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))) (pow (PI) 3))
7.0ms	c	@	inf	((* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ 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 (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))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (PI) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (- (+ 1 c) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))) (pow (PI) 3))
7.0ms	cosTheta	@	-inf	((* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ 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 (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))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (PI) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (- (+ 1 c) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))) (pow (PI) 3))
6.0ms	cosTheta	@	0	((* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ 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 (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))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (PI) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ 1 (sqrt (PI))) (- (+ 1 c) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))) (pow (PI) 3))

simplify1.0s (11.2%)

Memory

-197.9MiB live, 465.4MiB allocated; 1.1s collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	653	5480
1	2258	5299
0	8792	5080

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 119

Calls

Call 1

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

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

rewrite135.0ms (1.5%)

Memory

19.5MiB live, 208.6MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	71	506
0	122	502
1	462	449
0	3738	449

Stop Event

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

Counts

26 → 501

Calls

Call 1

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

Outputs
(.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32)))) (pow.f32 (exp.f32 cosTheta) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32))))
(.f32 (pow.f32 (exp.f32 cosTheta) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32))) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (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) (neg.f32 cosTheta)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))
(fma.f32 (cosh.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))
(fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (cosh.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 (.f32 (cosh.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sinh.f32 (.f32 (neg.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)) (cosh.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal 2 binary32) cosTheta) (.f32 #s(literal 2 binary32) cosTheta))) (+.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (.f32 #s(literal 2 binary32) cosTheta) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (fma.f32 (.f32 #s(literal 2 binary32) cosTheta) (.f32 #s(literal 2 binary32) cosTheta) (.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (*.f32 cosTheta cosTheta))) (neg.f32 (+.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))
(/.f32 (neg.f32 (-.f32 (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 (/.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 #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 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 3 binary32)) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 3 binary32)))) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 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 cosTheta) (neg.f32 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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 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 cosTheta) (neg.f32 cosTheta)) cosTheta) c))))
(/.f32 #s(literal 2 binary32) (*.f32 #s(literal 2 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (+.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 cosTheta) (neg.f32 cosTheta)) cosTheta) c)))))
(/.f32 #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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1 binary32))
(exp.f32 (*.f32 (log1p.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) 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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32)))))
(neg.f32 (/.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 cosTheta) (neg.f32 cosTheta)) cosTheta) c)))))
(/.f32 (-.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32))) (-.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal -1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) c) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) c))) (-.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 cosTheta) (neg.f32 cosTheta)) cosTheta) c)))
(/.f32 (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 3 binary32)) (pow.f32 (neg.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))) #s(literal 3 binary32))) (+.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (*.f32 (-.f32 c #s(literal -1 binary32)) (neg.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) c) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) c) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) c)) (.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 cosTheta) (neg.f32 cosTheta)) cosTheta) c)))))
(/.f32 (neg.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))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)))) (neg.f32 (-.f32 (-.f32 c #s(literal -1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 3 binary32)) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 c #s(literal -1 binary32))) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)))))
(/.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (*.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) c)))
(/.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (fma.f32 (neg.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) c)))
(/.f32 (fma.f32 (neg.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta)) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c)))
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(-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32))
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(/.f32 #s(literal 1 binary32) (pow.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(exp.f32 (*.f32 (log.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)))
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eval113.0ms (1.3%)

Memory: 1.3MiB live, 140.9MiB allocated; 28ms collecting garbage
Compiler: Compiled 30 027 to 2 878 computations (90.4% saved)

prune65.0ms (0.7%)

Memory

-3.3MiB live, 85.6MiB allocated; 13ms collecting garbage

Pruning

35 alts after pruning (32 fresh and 3 done)

	Pruned	Kept	Total
New	500	29	529
Fresh	16	3	19
Picked	2	3	5
Done	0	0	0
Total	518	35	553

Accuracy

100.0%

Counts

553 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32)))))
	98.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (*.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) c))))
▶	98.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
▶	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)))) cosTheta)))
✓	98.7%	(/.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 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	94.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	91.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	98.5%	(/.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)))))
	98.1%	(/.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)))))
✓	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	55.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (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)) c c)))
	98.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	91.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	56.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))))
	98.1%	(*.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
▶	97.8%	(*.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
	58.8%	(*.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))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta))))
	90.6%	(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) c)) #s(literal -1 binary32)))
	90.5%	(exp.f32 (*.f32 (log1p.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) c)) #s(literal -1 binary32)))
	94.9%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (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))
▶	92.3%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (.f32 (fma.f32 (sqrt.f32 (PI.f32)) (PI.f32) (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 3 binary32))) cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta)) (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)))))
	96.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (.f32 (-.f32 (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)) (PI.f32)) cosTheta) (-.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	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))
	96.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	48.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (.f32 (-.f32 (fma.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 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (/.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))) cosTheta)) (*.f32 cosTheta cosTheta))) cosTheta))
	56.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) c) (.f32 (fma.f32 (.f32 #s(literal -2 binary32) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (PI.f32)) (.f32 cosTheta cosTheta))) (neg.f32 c))) (.f32 c c))))
	56.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (/.f32 cosTheta c) (/.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) c) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 (.f32 (.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) cosTheta) (-.f32 #s(literal 2 binary32) (.f32 #s(literal 2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (PI.f32)) c) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))))) (*.f32 c c))))
	37.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (*.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32)) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)) (neg.f32 (fma.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 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta)))))))
	37.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (.f32 (-.f32 (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32)) (fma.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 (PI.f32)) (.f32 cosTheta cosTheta)))) (/.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) cosTheta)) (pow.f32 cosTheta #s(literal 3 binary32)))))

Compiler

Compiled 3 641 to 2 113 computations (42% saved)

simplify133.0ms (1.5%)

Memory

20.1MiB live, 160.7MiB allocated; 29ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
cost-diff	0	(fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32)))
cost-diff	0	(pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32))
cost-diff	22	(*.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
cost-diff	0	(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
cost-diff	1	(+.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))
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta))))
cost-diff	2	(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)
cost-diff	5	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
cost-diff	0	(PI.f32)
cost-diff	0	(sqrt.f32 (PI.f32))
cost-diff	0	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
cost-diff	0	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
cost-diff	0	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))
cost-diff	0	(fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 c c))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
cost-diff	5	(/.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	710
0	116	690
1	230	658
2	692	646
3	3114	646
0	8198	632

Stop Event

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

Calls

Call 1

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

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

localize335.0ms (3.7%)

Memory

-5.1MiB live, 617.7MiB allocated; 59ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.140625	(pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32))
accuracy	0.4616012695368841	(*.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #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 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
accuracy	0.5840225586106522	(fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32)))
accuracy	0.79296875	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	0.11362290172363414	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.265625	(/.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)))
accuracy	0.56640625	(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)
accuracy	0.79296875	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
accuracy	0.40365222071916723	#s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta))
accuracy	0.5625	(/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)
accuracy	0.62109375	(.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
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	0.3046875	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	2.2107120804609273	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.11362290172363414	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.265625	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
accuracy	0.28515625	(/.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c)))
accuracy	0.3046875	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

273.0ms

256×

valid

Compiler

Compiled 633 to 64 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-pow: 113.0ms (46.9% of total)

ival-mult: 41.0ms (17% of total)

ival-div: 30.0ms (12.4% of total)

ival-exp: 18.0ms (7.5% of total)

ival-add: 15.0ms (6.2% of total)

ival-sqrt: 10.0ms (4.1% of total)

ival-sub: 9.0ms (3.7% of total)

ival-neg: 2.0ms (0.8% of total)

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

exact: 1.0ms (0.4% of total)

adjust: 0.0ms (0% of total)

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

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

series85.0ms (0.9%)

Memory

23.0MiB live, 213.4MiB allocated; 22ms collecting garbage

Counts

24 → 179

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
24.0ms	cosTheta	@	inf	((/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))) (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) 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 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta))) (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta) (* (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2)) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
20.0ms	cosTheta	@	-inf	((/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))) (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) 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 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta))) (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta) (* (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2)) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
9.0ms	c	@	inf	((/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))) (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) 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 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta))) (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta) (* (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2)) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
8.0ms	c	@	0	((/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))) (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) 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 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta))) (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta) (* (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2)) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
7.0ms	cosTheta	@	0	((/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))) (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) 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 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta)) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta))) (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) cosTheta) (* (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2)) (pow (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) -1/2) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) (- c -1)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI)))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))

simplify298.0ms (3.3%)

Memory

-8.0MiB live, 403.8MiB allocated; 76ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1193	12728
1	4349	12559
0	9441	11921

Stop Event

1×	iter limit
1×	node limit

Counts

179 → 178

Calls

Call 1

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

rewrite163.0ms (1.8%)

Memory

5.4MiB live, 247.8MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	500
0	116	476
1	455	439
0	3919	434

Stop Event

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

Counts

24 → 519

Calls

Call 1

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

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

eval128.0ms (1.4%)

Memory: 15.3MiB live, 255.4MiB allocated; 72ms collecting garbage
Compiler: Compiled 49 669 to 3 705 computations (92.5% saved)

prune105.0ms (1.2%)

Memory

15.7MiB live, 106.9MiB allocated; 20ms collecting garbage

Pruning

41 alts after pruning (37 fresh and 4 done)

	Pruned	Kept	Total
New	761	20	781
Fresh	10	17	27
Picked	4	1	5
Done	0	3	3
Total	775	41	816

Accuracy

100.0%

Counts

816 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	59.0%	(pow.f32 (pow.f32 (/.f32 (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))) (-.f32 #s(literal 1 binary32) c)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal 2 binary32)) #s(literal -1/2 binary32))
▶	98.9%	(/.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
	98.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) c)) (/.f32 (-.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (.f32 (/.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32)))))
	63.0%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32))) (.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32))))) (.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32))))))
	97.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
	92.2%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (-.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
✓	98.7%	(/.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 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
▶	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	94.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	91.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
▶	98.5%	(/.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)))))
	98.1%	(/.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)))))
✓	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))))) cosTheta))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))) #s(literal 2 binary32))) (.f32 (-.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)))))
	95.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (pow.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))) #s(literal 3 binary32)) (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 3 binary32))) (.f32 (fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))) (-.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	36.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta) (.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (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) (/.f32 #s(literal 1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))))
	55.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (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)) c c)))
	98.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
▶	91.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.7%	(*.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/4 binary32)) #s(literal 2 binary32)))
	98.7%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 #s(literal 1 binary32) c))
	98.8%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32))))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 #s(literal 1 binary32) c))
▶	89.5%	(exp.f32 (.f32 (log1p.f32 (+.f32 #s(approx ( (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)) c)) #s(literal -1 binary32)))
	98.6%	#s(approx (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (/.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	96.3%	#s(approx (/ 1 (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c)))) (.f32 (fma.f32 (fma.f32 (.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) #s(literal 1/2 binary32)) (/.f32 (fma.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (neg.f32 (-.f32 #s(literal 1 binary32) c))) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) c) (-.f32 #s(literal 1 binary32) c))) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	94.9%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (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))
	90.3%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (.f32 (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) cosTheta))
✓	92.3%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (.f32 (fma.f32 (sqrt.f32 (PI.f32)) (PI.f32) (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 3 binary32))) cosTheta) (fma.f32 (sqrt.f32 (PI.f32)) (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta)) (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)))))
	96.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (.f32 (-.f32 (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)) (PI.f32)) cosTheta) (-.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	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))
	48.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (.f32 (-.f32 (fma.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 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (/.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))) cosTheta)) (*.f32 cosTheta cosTheta))) cosTheta))
	56.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) c) (.f32 (fma.f32 (.f32 #s(literal -2 binary32) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (PI.f32)) (.f32 cosTheta cosTheta))) (neg.f32 c))) (.f32 c c))))
	37.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (*.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32)) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)) (neg.f32 (fma.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 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta)))))))

Compiler

Compiled 4 215 to 2 412 computations (42.8% saved)

simplify188.0ms (2.1%)

Memory

12.0MiB live, 188.2MiB allocated; 62ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f32 (.f32 (log1p.f32 (+.f32 #s(approx ( (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)) c)) #s(literal -1 binary32)))
cost-diff	1	(.f32 (log1p.f32 (+.f32 #s(approx ( (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)) c)) #s(literal -1 binary32))
cost-diff	2	(/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)
cost-diff	4	(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
cost-diff	1	(.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
cost-diff	1	(-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 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))) cosTheta)
cost-diff	0	#s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 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) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
cost-diff	0	(*.f32 (-.f32 #s(literal 1 binary32) c) cosTheta)
cost-diff	0	(.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))
cost-diff	0	(/.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
cost-diff	2	(.f32 #s(literal 1 binary32) (.f32 (*.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	805
0	136	801
1	244	799
2	627	778
3	2164	752
0	8704	739

Stop Event

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

Calls

Call 1

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

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

localize333.0ms (3.7%)

Memory

-72.0MiB live, 445.1MiB allocated; 118ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.40365222071916723	#s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta))
accuracy	0.5625	(/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)
accuracy	1.0	(pow.f32 (PI.f32) #s(literal -1/2 binary32))
accuracy	2.99459481422393	(exp.f32 (.f32 (log1p.f32 (+.f32 #s(approx ( (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)) c)) #s(literal -1 binary32)))
accuracy	0.046875	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
accuracy	0.11362290172363414	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.265625	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.3671875	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	0.2578125	(/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.265625	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
accuracy	0.3046875	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.42359655321221285	#s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)))
accuracy	0.265625	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
accuracy	0.6328125	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	2.2116343886734136	#s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
accuracy	0.11362290172363414	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.1171875	(/.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
accuracy	0.27734375	(.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	0.29916000976844204	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))

Samples

141.0ms	231×	0	valid
35.0ms	25×	1	valid

Compiler

Compiled 647 to 67 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 150.0ms

ival-mult: 37.0ms (24.7% of total)

ival-sub: 33.0ms (22% of total)

ival-div: 26.0ms (17.3% of total)

ival-pow: 15.0ms (10% of total)

ival-exp: 12.0ms (8% of total)

ival-add: 10.0ms (6.7% of total)

ival-sqrt: 6.0ms (4% of total)

adjust: 5.0ms (3.3% of total)

ival-log1p: 3.0ms (2% of total)

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

exact: 1.0ms (0.7% of total)

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

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

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

series96.0ms (1.1%)

Memory

43.5MiB live, 132.8MiB allocated; 15ms collecting garbage

Counts

28 → 176

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
31.0ms	c	@	0	((* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (* (* (- 1 c) cosTheta) (sqrt (PI))) (* (- 1 c) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (+ 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)))) (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) (/ (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) cosTheta) (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1) (exp (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1)) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (PI) -1/2) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
25.0ms	cosTheta	@	inf	((* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (* (* (- 1 c) cosTheta) (sqrt (PI))) (* (- 1 c) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (+ 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)))) (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) (/ (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) cosTheta) (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1) (exp (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1)) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (PI) -1/2) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
11.0ms	cosTheta	@	-inf	((* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (* (* (- 1 c) cosTheta) (sqrt (PI))) (* (- 1 c) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (+ 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)))) (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) (/ (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) cosTheta) (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1) (exp (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1)) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (PI) -1/2) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
11.0ms	c	@	inf	((* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (* (* (- 1 c) cosTheta) (sqrt (PI))) (* (- 1 c) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (+ 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)))) (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) (/ (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) cosTheta) (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1) (exp (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1)) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (PI) -1/2) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))
6.0ms	cosTheta	@	0	((* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (* (* (- 1 c) cosTheta) (sqrt (PI))) (* (- 1 c) cosTheta) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (+ 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)))) (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) (/ (+ (* (pow (PI) -1/2) (- 1 cosTheta)) (* (* cosTheta cosTheta) (* (pow (PI) -1/2) (+ (* 1/2 cosTheta) -3/2)))) cosTheta) (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1) (exp (* (log (+ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) c))) -1)) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))) (- (- 1 cosTheta) cosTheta) (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (pow (PI) -1/2) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))

simplify221.0ms (2.5%)

Memory

1.6MiB live, 371.7MiB allocated; 68ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1068	10030
1	3873	9932
0	8478	9401

Stop Event

1×	iter limit
1×	node limit

Counts

176 → 174

Calls

Call 1

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

Outputs
(* (* cosTheta (- 1 c)) (sqrt (PI)))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* (* cosTheta (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c))))) (sqrt (PI)))))
(.f32 (.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* (sqrt (PI)) (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c))))) (* (* cosTheta (- (+ 1/2 (/ 1 (- 1 c))) (+ (/ c (- 1 c)) (/ (* (+ (* -1 (- 1 c)) (* (sqrt (PI)) (- 1 (pow c 2)))) (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c))))) (- 1 c))))) (sqrt (PI)))))))
(.f32 (fma.f32 (fma.f32 (.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) (/.f32 (fma.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (neg.f32 (-.f32 #s(literal 1 binary32) c))) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) c) (-.f32 #s(literal 1 binary32) c))) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* cosTheta (+ (* (sqrt (PI)) (- (+ 1/2 (/ 1 (- 1 c))) (+ (/ c (- 1 c)) (/ (* (+ (* -1 (- 1 c)) (* (sqrt (PI)) (- 1 (pow c 2)))) (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c))))) (- 1 c))))) (* (* cosTheta (- 1/2 (+ (* -1 (/ (- c 1) (- 1 c))) (+ (/ (* (+ (* -1 (- 1 c)) (* (sqrt (PI)) (- 1 (pow c 2)))) (- (+ 1/2 (/ 1 (- 1 c))) (+ (/ c (- 1 c)) (/ (* (+ (* -1 (- 1 c)) (* (sqrt (PI)) (- 1 (pow c 2)))) (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c))))) (- 1 c))))) (- 1 c)) (/ (* (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c)))) (- (+ c (* -1/2 (- 1 c))) 1)) (- 1 c)))))) (sqrt (PI))))) (* (sqrt (PI)) (- 1 (* (sqrt (PI)) (/ (- 1 (pow c 2)) (- 1 c)))))))))
(.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 (fma.f32 #s(literal -1 binary32) (-.f32 c #s(literal 1 binary32)) (fma.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) (/.f32 (fma.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (neg.f32 (-.f32 #s(literal 1 binary32) c))) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) c) (-.f32 #s(literal 1 binary32) c))) (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (neg.f32 (-.f32 #s(literal 1 binary32) c))) (.f32 (-.f32 (fma.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) c) c) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))))))) (-.f32 #s(literal 1 binary32) c))) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) (/.f32 (fma.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (neg.f32 (-.f32 #s(literal 1 binary32) c))) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) c) (-.f32 #s(literal 1 binary32) c))) (sqrt.f32 (PI.f32)))) cosTheta (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* cosTheta (- 1 c))
(*.f32 (-.f32 #s(literal 1 binary32) c) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 (PI.f32) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)))) 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 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))) (*.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (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 (sqrt.f32 (PI.f32))) (.f32 (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (PI.f32))))) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))) cosTheta (.f32 (neg.f32 (PI.f32)) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #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)
(/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) cosTheta)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
-1
#s(literal -1 binary32)
(- (* -3/2 cosTheta) 1)
(-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32))
(- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1)
(-.f32 (*.f32 (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)) cosTheta) #s(literal 1 binary32))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) 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)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(fma.f32 (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))
(fma.f32 (fma.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (fma.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta))))
(neg.f32 (+.f32 (neg.f32 (log.f32 cosTheta)) (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(+ (* -1 (* (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (sqrt (PI)))) (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))))
(neg.f32 (fma.f32 cosTheta (*.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (+.f32 (neg.f32 (log.f32 cosTheta)) (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(+ (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))) (* cosTheta (+ (* -1 (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* -1/2 (* cosTheta (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))
(fma.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) cosTheta) (fma.f32 (neg.f32 (PI.f32)) (pow.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (*.f32 (neg.f32 (sqrt.f32 (PI.f32))) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)))) cosTheta (neg.f32 (+.f32 (neg.f32 (log.f32 cosTheta)) (log.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(+ (* -1 (+ (log (sqrt (/ 1 (PI)))) (* -1 (log cosTheta)))) (* cosTheta (+ (* -1 (* (sqrt (PI)) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (+ (* -1/2 (+ (* -1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 2 (* (sqrt (PI)) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* -1/6 (* cosTheta (+ (* -6 (* (PI) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (+ (* 2 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))) (* 6 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))))))
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(* (* cosTheta (- 1 (pow c 2))) (sqrt (PI)))
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(+ (* -1 (log (+ 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) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (* -1/24 (/ (+ (* -3 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (* -3 (/ (* 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))))) 2)))))) (pow cosTheta 4)))))
(fma.f32 (log1p.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c)) #s(literal -1 binary32) (fma.f32 (/.f32 (.f32 #s(literal -3 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))) (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) cosTheta) (PI.f32)) (.f32 (pow.f32 (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32)) #s(literal 2 binary32)) #s(literal -2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))) #s(literal -1/24 binary32) (.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (+.f32 (fma.f32 (.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32)) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/2 binary32))))
(+ (* -1 (log (+ 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) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* -1/24 (/ (+ (* -3 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (* -3 (/ (* 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))))) 2)))))) (pow cosTheta 4))) (* -1/720 (/ (+ (* 30 (* (sqrt (/ (pow cosTheta 3) (pow (PI) 3))) (/ (pow (exp (* -1 (pow cosTheta 2))) 3) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (+ (* 45 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (* 45 (/ (* (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))))) 2))))))) (pow cosTheta 6))))))
(+.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (.f32 (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32)) (sqrt.f32 #s(literal -2 binary32)))) #s(literal -1/2 binary32) (neg.f32 (log1p.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c)))) (fma.f32 (/.f32 (fma.f32 #s(literal 45 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (.f32 (/.f32 (pow.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) (.f32 (PI.f32) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 4 binary32)))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32)) #s(literal 2 binary32))))) (.f32 (.f32 #s(literal 30 binary32) (sqrt.f32 (pow.f32 (/.f32 cosTheta (PI.f32)) #s(literal 3 binary32)))) (pow.f32 (/.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32))) #s(literal 3 binary32)))) (pow.f32 cosTheta #s(literal 6 binary32))) #s(literal -1/720 binary32) (.f32 (/.f32 (.f32 #s(literal -3 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))) (+.f32 (fma.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (/.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 2 binary32)) cosTheta) (PI.f32)) (.f32 (pow.f32 (+.f32 (fma.f32 (.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) c) #s(literal 1 binary32)) #s(literal 2 binary32)) #s(literal -2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))) #s(literal -1/24 binary32))))
(* -2 cosTheta)
(*.f32 #s(literal -2 binary32) cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta)
(* (sqrt cosTheta) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(.f32 (.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 cosTheta))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(.f32 (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32)))))) cosTheta)
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(.f32 (fma.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (fma.f32 (.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (sqrt.f32 #s(literal -2 binary32)) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (sqrt.f32 #s(literal -2 binary32))))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/2 binary32)) #s(literal -1/8 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/2 binary32)) #s(literal -1/8 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))))) #s(literal 1/16 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (PI.f32))))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))))))
(* (sqrt (/ 1 cosTheta)) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))
(fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
(fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/2 binary32)) #s(literal -1/8 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) #s(literal 1/2 binary32) (*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
(fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -2 binary32))) #s(literal -1/2 binary32)) #s(literal -1/8 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))) #s(literal 1/16 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 3 binary32))))) #s(literal 1/2 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))))
(* -1 (* (sqrt (PI)) (/ (- 1 c) (+ (* -1 (* (sqrt (PI)) (- 1 (pow c 2)))) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (* (sqrt 2) (- 1 c))) (exp (pow cosTheta 2))))))))
(/.f32 (neg.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) c))) (fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 c c))) (sqrt.f32 (PI.f32)) (.f32 (/.f32 (.f32 (*.f32 (sqrt.f32 #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))))
(+ (* -1 (* (sqrt (PI)) (/ (- 1 c) (+ (* -1 (* (sqrt (PI)) (- 1 (pow c 2)))) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (* (sqrt 2) (- 1 c))) (exp (pow cosTheta 2)))))))) (* 1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (* (sqrt -1) (pow (- 1 c) 2)) (* (exp (pow cosTheta 2)) (* (sqrt 2) (pow (+ (* -1 (* (sqrt (PI)) (- 1 (pow c 2)))) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (* (sqrt 2) (- 1 c))) (exp (pow cosTheta 2))))) 2)))))))
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cosTheta
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(/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal 1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
(* -1 (+ (log -1) (* -1 (log (/ -1 c)))))
(fma.f32 #s(literal 1 binary32) (log.f32 (/.f32 #s(literal -1 binary32) c)) (neg.f32 (log.f32 #s(literal -1 binary32))))
(+ (* -1 (+ (log -1) (* -1 (log (/ -1 c))))) (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)))
(neg.f32 (+.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c) (fma.f32 (log.f32 (/.f32 #s(literal -1 binary32) c)) #s(literal -1 binary32) (log.f32 #s(literal -1 binary32)))))
(+ (* -1 (+ (log -1) (* -1 (log (/ -1 c))))) (* -1 (/ (+ 1 (+ (* -1/2 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c)) (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)))
(neg.f32 (+.f32 (/.f32 (+.f32 (fma.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) c) #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta))) #s(literal 1 binary32)) c) (fma.f32 (log.f32 (/.f32 #s(literal -1 binary32) c)) #s(literal -1 binary32) (log.f32 #s(literal -1 binary32)))))
(+ (* -1 (+ (log -1) (* -1 (log (/ -1 c))))) (* -1 (/ (+ 1 (+ (* -1 (/ (+ (* -1/3 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c)) (* 1/2 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) c)) (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)))
(neg.f32 (+.f32 (/.f32 (+.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) #s(literal -1/3 binary32) (.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 2 binary32)) #s(literal 1/2 binary32))) (neg.f32 c))) #s(literal 1 binary32)) c) (fma.f32 (log.f32 (/.f32 #s(literal -1 binary32) c)) #s(literal -1 binary32) (log.f32 #s(literal -1 binary32)))))

rewrite166.0ms (1.8%)

Memory

-38.6MiB live, 263.1MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	534
0	136	531
1	489	515
0	3737	506

Stop Event

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

Counts

28 → 378

Calls

Call 1

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

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

eval89.0ms (1%)

Memory: 4.0MiB live, 238.8MiB allocated; 20ms collecting garbage
Compiler: Compiled 31 239 to 3 051 computations (90.2% saved)

prune110.0ms (1.2%)

Memory

4.8MiB live, 193.0MiB allocated; 16ms collecting garbage

Pruning

45 alts after pruning (40 fresh and 5 done)

	Pruned	Kept	Total
New	532	19	551
Fresh	11	21	32
Picked	4	1	5
Done	0	4	4
Total	547	45	592

Accuracy

100.0%

Counts

592 → 45

Alt Table

Click to see full alt table

Status	Accuracy	Program
	92.0%	(/.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) c) cosTheta) (sqrt.f32 (PI.f32)))) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
	98.9%	(/.f32 (.f32 #s(literal 1 binary32) (.f32 #s(approx (* (- 1 c) cosTheta) (fma.f32 (neg.f32 cosTheta) c cosTheta)) (sqrt.f32 (PI.f32)))) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
	98.7%	(/.f32 (.f32 #s(literal 1 binary32) (.f32 #s(approx (* (- 1 c) cosTheta) (.f32 (fma.f32 #s(literal -1 binary32) cosTheta (/.f32 cosTheta c)) c)) (sqrt.f32 (PI.f32)))) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
	98.6%	(/.f32 #s(approx (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (.f32 (-.f32 (/.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) c) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) cosTheta) (-.f32 (fma.f32 c c #s(literal 1 binary32)) c) (.f32 (sqrt.f32 (PI.f32)) (+.f32 (pow.f32 c #s(literal 3 binary32)) #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) (-.f32 (fma.f32 c c #s(literal 1 binary32)) c))))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) cosTheta) (-.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) c))))
	97.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (.f32 (-.f32 #s(literal 1 binary32) c) (neg.f32 #s(approx ( (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32)))))) (.f32 (neg.f32 (sqrt.f32 (PI.f32))) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) c)))))
	97.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)) (.f32 (-.f32 #s(literal 1 binary32) c) #s(approx ( (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (-.f32 #s(literal 1 binary32) c) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
	92.2%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (-.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (-.f32 #s(literal 1 binary32) c))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) cosTheta)))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (*.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	98.7%	(/.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 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32))))))
	94.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	91.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))
	98.1%	(/.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)))))
✓	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32)))) #s(literal 2 binary32))) (.f32 (-.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (.f32 cosTheta cosTheta) (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (fma.f32 #s(literal 1/2 binary32) cosTheta #s(literal -3/2 binary32))))) cosTheta)))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	36.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) (* (* cosTheta cosTheta) (+ (* (sqrt (/ 1 (PI))) -3/2) (* (* 1/2 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta) (.f32 (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 #s(literal 3/2 binary32) (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) (/.f32 #s(literal 1 binary32) cosTheta))) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))))))
	91.4%	(/.f32 #s(literal 1 binary32) #s(approx (/ (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta)) (- 1 c)) (* (* (sqrt (PI)) cosTheta) (- 1 (* c c)))) (* (* (sqrt (PI)) cosTheta) (- 1 c))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))))
	55.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (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)) c c)))
	98.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	97.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	91.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (*.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))) cosTheta)))
✓	91.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	92.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	97.7%	(*.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/4 binary32)) #s(literal 2 binary32)))
	97.0%	(.f32 (pow.f32 (+.f32 (/.f32 #s(approx ( (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (+.f32 (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
	91.4%	(.f32 (pow.f32 #s(approx (+ (+ 1 c) (/ ( (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1/2 binary32)) (pow.f32 #s(approx (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI))))) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal -1/2 binary32)))
	98.7%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 #s(literal 1 binary32) c))
	57.8%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 (/.f32 #s(approx ( (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (/.f32 #s(approx (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	89.5%	(exp.f32 (.f32 (log1p.f32 (+.f32 (/.f32 #s(approx ( (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta #s(literal -1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) #s(literal -1 binary32)))
	98.6%	#s(approx (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (/.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	96.3%	#s(approx (/ (* 1 (* (* (- 1 c) cosTheta) (sqrt (PI)))) (+ (* (- 1 c) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (pow (exp cosTheta) cosTheta))) (* (* (- 1 (* c c)) cosTheta) (sqrt (PI))))) (.f32 (fma.f32 (fma.f32 (.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) (/.f32 (fma.f32 (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (sqrt.f32 (PI.f32)) (neg.f32 (-.f32 #s(literal 1 binary32) c))) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) c) (-.f32 #s(literal 1 binary32) c))) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (-.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	94.9%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (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))
	90.3%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (.f32 (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) cosTheta))
✓	92.3%	#s(approx (/ 1 (+ (+ 1 c) (/ (* (pow (exp cosTheta) (neg cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta))) (* cosTheta (sqrt (PI)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	96.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 (.f32 (-.f32 (pow.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) #s(literal 2 binary32)) (PI.f32)) cosTheta) (-.f32 (.f32 (-.f32 (.f32 (fma.f32 (pow.f32 (-.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal -1 binary32)) #s(literal 2 binary32)) (neg.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (*.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (neg.f32 cosTheta)) (fma.f32 (-.f32 c (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (PI.f32) (PI.f32))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	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))
	48.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) (.f32 (-.f32 (fma.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 #s(literal 3/2 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (/.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))) cosTheta)) (*.f32 cosTheta cosTheta))) cosTheta))
	56.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (pow.f32 cosTheta #s(literal 3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) cosTheta (sqrt.f32 (PI.f32))) c) (.f32 (fma.f32 (.f32 #s(literal -2 binary32) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (PI.f32)) (.f32 cosTheta cosTheta))) (neg.f32 c))) (.f32 c c))))
	37.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (- (* (neg cosTheta) (+ (* (neg (sqrt (pow (PI) 3))) (pow (- (+ 1 c) (sqrt (/ 1 (PI)))) 2)) (* (sqrt (/ 1 (PI))) (* -3/2 (PI))))) (+ (* (- c (sqrt (/ 1 (PI)))) (PI)) (PI))) cosTheta) (sqrt (PI))) cosTheta) (*.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32)) (fma.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)) (neg.f32 (fma.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 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta)))))))

Compiler

Compiled 6 851 to 2 029 computations (70.4% saved)

regimes180.0ms (2%)

Memory

-2.4MiB live, 290.9MiB allocated; 37ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

39.0ms	(/.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)))))
37.0ms	(.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)))
34.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
24.0ms	cosTheta
23.0ms	c

Results

Accuracy	Segments	Branch
98.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
98.9%	1	`(+.f32 #s(literal 1 binary32) c)`
98.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.9%	1	`cosTheta`
98.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes95.0ms (1.1%)

Memory

33.2MiB live, 163.3MiB allocated; 22ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

17.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
17.0ms	cosTheta
15.0ms	(+.f32 #s(literal 1 binary32) c)
14.0ms	c
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)))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes138.0ms (1.5%)

Memory

-27.3MiB live, 217.0MiB allocated; 30ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

23.0ms	(+.f32 #s(literal 1 binary32) c)
21.0ms	c
16.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
15.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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)))

Results

Accuracy	Segments	Branch
98.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
98.7%	1	`(+.f32 #s(literal 1 binary32) c)`
98.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.7%	1	`cosTheta`
98.7%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes88.0ms (1%)

Memory

42.6MiB live, 232.6MiB allocated; 19ms collecting garbage

Counts

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

17.0ms	cosTheta
15.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
15.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
13.0ms	c
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)))))

Results

Accuracy	Segments	Branch
98.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.7%	1	`cosTheta`
98.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
98.7%	1	`(+.f32 #s(literal 1 binary32) c)`
98.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.7%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes64.0ms (0.7%)

Memory

-20.0MiB live, 117.8MiB allocated; 7ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

15.0ms	(+.f32 #s(literal 1 binary32) c)
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)))))
10.0ms	c
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
98.6%	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)))))`
98.6%	1	`cosTheta`
98.6%	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)))`
98.6%	1	`(+.f32 #s(literal 1 binary32) c)`
98.6%	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))))`
98.6%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes91.0ms (1%)

Memory

0.2MiB live, 108.3MiB allocated; 20ms collecting garbage

Counts

32 → 1

Calls

Call 1

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

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:

36.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
22.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	c
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
8.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes55.0ms (0.6%)

Memory

26.7MiB live, 115.7MiB allocated; 10ms collecting garbage

Counts

31 → 1

Calls

Call 1

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

Outputs

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

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes178.0ms (2%)

Memory

-35.4MiB live, 105.3MiB allocated; 24ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

70.0ms	(/.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)))))
45.0ms	c
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes78.0ms (0.9%)

Memory

-6.4MiB live, 94.1MiB allocated; 15ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

34.0ms	(.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 #s(literal 1 binary32) c)
8.0ms	c
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
7.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
97.6%	1	`(+.f32 #s(literal 1 binary32) c)`
97.6%	1	`c`
97.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.6%	1	`cosTheta`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes36.0ms (0.4%)

Memory

40.5MiB live, 85.2MiB allocated; 6ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
5.0ms	c
5.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
5.0ms	(.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)))
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.6%	1	`(+.f32 #s(literal 1 binary32) c)`
97.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.6%	1	`cosTheta`
97.6%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes29.0ms (0.3%)

Memory

1.8MiB live, 91.8MiB allocated; 6ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

6.0ms	c
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))))
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes27.0ms (0.3%)

Memory

-33.5MiB live, 73.9MiB allocated; 4ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

6.0ms	c
5.0ms	(/.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 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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	cosTheta

Results

Accuracy	Segments	Branch
94.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
94.9%	1	`cosTheta`
94.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
94.9%	1	`(+.f32 #s(literal 1 binary32) c)`
94.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
94.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes23.0ms (0.3%)

Memory

-5.5MiB live, 85.1MiB allocated; 6ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
94.8%	1	`(+.f32 #s(literal 1 binary32) c)`
94.8%	1	`c`
94.8%	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)))`
94.8%	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))))`
94.8%	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)))))`
94.8%	1	`cosTheta`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes31.0ms (0.3%)

Memory

-8.9MiB live, 55.5MiB allocated; 34ms collecting garbage

Counts

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

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

Calls

6 calls:

19.0ms	cosTheta
2.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
2.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
2.0ms	c

Results

Accuracy	Segments	Branch
92.3%	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)))))`
92.3%	1	`cosTheta`
92.3%	1	`c`
92.3%	1	`(+.f32 #s(literal 1 binary32) c)`
92.3%	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)))`
92.3%	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))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes7.0ms (0.1%)

Memory

30.3MiB live, 30.3MiB allocated; 0ms collecting garbage

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 (.f32 (/.f32 #s(literal 1 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	cosTheta
1.0ms	c

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify68.0ms (0.8%)

Memory

-6.0MiB live, 127.2MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	528
1	228	522
2	570	506
3	2445	506

Stop Event

1×	node limit

Calls

Call 1

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

derivations501.0ms (5.6%)

Memory

-14.5MiB live, 511.2MiB allocated; 42ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 528 to 134 computations (74.6% saved)

preprocess76.0ms (0.8%)

Memory: 7.6MiB live, 111.2MiB allocated; 22ms collecting garbage
Compiler: Compiled 1 106 to 304 computations (72.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze58.0ms (0.6%)

sample2.0s (21.8%)

explain231.0ms (2.6%)

preprocess162.0ms (1.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify129.0ms (1.4%)

localize61.0ms (0.7%)

series34.0ms (0.4%)

simplify294.0ms (3.3%)

rewrite72.0ms (0.8%)

eval21.0ms (0.2%)

prune17.0ms (0.2%)

simplify145.0ms (1.6%)

localize231.0ms (2.6%)

series57.0ms (0.6%)

simplify1.0s (11.2%)

rewrite135.0ms (1.5%)

eval113.0ms (1.3%)

prune65.0ms (0.7%)

simplify133.0ms (1.5%)

localize335.0ms (3.7%)

series85.0ms (0.9%)

simplify298.0ms (3.3%)

rewrite163.0ms (1.8%)

eval128.0ms (1.4%)

prune105.0ms (1.2%)

simplify188.0ms (2.1%)

localize333.0ms (3.7%)

series96.0ms (1.1%)

simplify221.0ms (2.5%)

rewrite166.0ms (1.8%)

eval89.0ms (1%)

prune110.0ms (1.2%)

regimes180.0ms (2%)

regimes95.0ms (1.1%)

regimes138.0ms (1.5%)

regimes88.0ms (1%)

regimes64.0ms (0.7%)

regimes91.0ms (1%)

regimes55.0ms (0.6%)

regimes178.0ms (2%)

regimes78.0ms (0.9%)

regimes36.0ms (0.4%)

regimes29.0ms (0.3%)

regimes27.0ms (0.3%)

regimes23.0ms (0.3%)

regimes31.0ms (0.3%)

regimes7.0ms (0.1%)

simplify68.0ms (0.8%)

derivations501.0ms (5.6%)

preprocess76.0ms (0.8%)

end0.0ms (0%)

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