Metrics for Beckmann Sample, normalization factor

analyze25.0ms (0.2%)

Memory

19.0MiB live, 58.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.0s (14.5%)

Memory

71.3MiB live, 3 030.7MiB allocated

Samples

1.5s	8 256×	0	valid
7.0ms	56×	0	invalid

Precisions

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

ival-div: 250.0ms (19.4% of total)

ival-add: 242.0ms (18.8% of total)

ival-mult: 176.0ms (13.6% of total)

const: 149.0ms (11.6% of total)

ival-sqrt: 118.0ms (9.1% of total)

ival-sub: 102.0ms (7.9% of total)

ival-exp: 77.0ms (6% of total)

ival-<: 70.0ms (5.4% of total)

ival-neg: 38.0ms (2.9% of total)

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

ival-and: 20.0ms (1.6% of total)

exact: 13.0ms (1% of total)

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

Bogosity

preprocess239.0ms (1.7%)

Memory

8.7MiB live, 212.6MiB allocated

Algorithm

2×	egg-herbie

Rules

1 608×	`accelerator-lowering-fma.f32`
1 608×	`accelerator-lowering-fma.f64`
1 468×	`div-sub`
1 040×	`-lowering-.f32`
1 040×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	152
1	140	140
2	404	133
3	1334	132
4	3715	132
5	5337	132
6	7076	132
7	7836	132
0	18	25
1	44	23
2	106	22
3	226	22
4	349	22
5	727	22
6	1873	22
7	2807	22
8	3448	22
9	4078	22
10	4244	22
11	4279	22
12	4312	22
13	4446	22
14	5067	22
15	5075	22
16	5079	22
17	5079	22
0	5079	21

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))

Outputs

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

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

Call 2

Inputs
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 (neg cosTheta)) (neg cosTheta))) (neg cosTheta))) (exp (* (neg (neg cosTheta)) (neg cosTheta))))))
(/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(neg (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 (neg cosTheta)) (neg cosTheta))) (neg cosTheta))) (exp (* (neg (neg cosTheta)) (neg cosTheta)))))))
(neg (/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))))
(/ 1 (+ (+ 1 cosTheta) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 c) c)) c)) (exp (* (neg c) c)))))

Outputs
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(/ 1 (+ (+ 1 c) (/ (sqrt (- 1 (+ cosTheta cosTheta))) (* (pow (exp cosTheta) cosTheta) (* (sqrt (PI)) cosTheta)))))
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 (neg cosTheta)) (neg cosTheta))) (neg cosTheta))) (exp (* (neg (neg cosTheta)) (neg cosTheta))))))
(/ 1 (- (+ 1 c) (/ (sqrt (+ 1 (+ cosTheta cosTheta))) (* (pow (exp cosTheta) cosTheta) (* (sqrt (PI)) cosTheta)))))
(/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(/ 1 (+ (/ (sqrt (- 1 (+ cosTheta cosTheta))) (* (pow (exp cosTheta) cosTheta) (* (sqrt (PI)) cosTheta))) (- 1 c)))
(neg (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 (neg cosTheta)) (neg cosTheta))) (neg cosTheta))) (exp (* (neg (neg cosTheta)) (neg cosTheta)))))))
(/ 1 (+ (- -1 c) (/ (sqrt (+ 1 (+ cosTheta cosTheta))) (* (pow (exp cosTheta) cosTheta) (* (sqrt (PI)) cosTheta)))))
(neg (/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))))
(/ 1 (- (+ c -1) (/ (sqrt (- 1 (+ cosTheta cosTheta))) (* (pow (exp cosTheta) cosTheta) (* (sqrt (PI)) cosTheta)))))
(/ 1 (+ (+ 1 cosTheta) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 c) c)) c)) (exp (* (neg c) c)))))
(/ 1 (+ (+ 1 cosTheta) (/ (sqrt (+ 1 (* c -2))) (* (pow (exp c) c) (* c (sqrt (PI)))))))

explain274.0ms (2%)

Memory

1.8MiB live, 447.3MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

114.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

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

ival-sqrt: 45.0ms (46.8% of total)

ival-pi: 13.0ms (13.5% of total)

ival-mult: 11.0ms (11.4% of total)

ival-div: 9.0ms (9.4% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	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) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

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) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify166.0ms (1.2%)

Memory

-13.0MiB live, 100.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	64	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	352	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))

Rules

1 608×	`accelerator-lowering-fma.f32`
1 608×	`accelerator-lowering-fma.f64`
1 040×	`-lowering-.f32`
1 040×	`-lowering-.f64`
978×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	126
1	44	118
2	106	115
3	226	115
4	349	115
5	727	115
6	1873	115
7	2807	115
8	3448	115
9	4078	115
10	4244	115
11	4279	115
12	4312	115
13	4446	115
14	5067	115
15	5075	115
16	5079	115
17	5079	115
0	5079	108

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
1
(+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))
(+ 1 c)
c
(* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))
(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
(/ 1 (sqrt (PI)))
(sqrt (PI))
(PI)
(/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(exp (* (neg cosTheta) cosTheta))
(* (neg cosTheta) cosTheta)
(neg cosTheta)

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

localize113.0ms (0.8%)

Memory

-10.3MiB live, 107.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.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)))))
✓	accuracy	98.1%	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))

Samples

86.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-add: 25.0ms (57.4% of total)

ival-div: 5.0ms (11.5% of total)

ival-mult: 4.0ms (9.2% of total)

ival-sqrt: 3.0ms (6.9% of total)

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

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

ival-pi: 1.0ms (2.3% of total)

ival-neg: 1.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

16.3MiB live, 55.0MiB allocated

Counts

6 → 84

Calls

Call 1

Inputs
#<alt (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))>
#<alt (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))>
#<alt (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))>
#<alt (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))>
#<alt (/ 1 (sqrt (PI)))>
#<alt (- (- 1 cosTheta) cosTheta)>

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

Calls

21 calls:

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

rewrite381.0ms (2.8%)

Memory

8.1MiB live, 561.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 132×	`accelerator-lowering-fma.f32`
4 132×	`accelerator-lowering-fma.f64`
3 752×	`-lowering-.f32`
3 752×	`-lowering-.f64`
3 536×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	89
1	126	80
2	1045	73
0	8542	73

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 473

Calls

Call 1

Inputs
(* (/ 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))))
(/ 1 (sqrt (PI)))
(- (- 1 cosTheta) cosTheta)

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

simplify431.0ms (3.1%)

Memory

-51.9MiB live, 784.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 656×	`accelerator-lowering-fma.f32`
9 656×	`accelerator-lowering-fma.f64`
5 090×	`-lowering-.f32`
5 090×	`-lowering-.f64`
4 540×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

eval120.0ms (0.9%)

Memory: 16.7MiB live, 210.1MiB allocated
Compiler: Compiled 23 196 to 2 836 computations (87.8% saved)

prune156.0ms (1.1%)

Memory

6.4MiB live, 241.8MiB allocated

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	529	28	557
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	530	28	558

Accuracy

99.9%

Counts

558 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	35.2%	(/.f32 (fma.f32 (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal -1 binary32) (neg.f32 c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))) (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))))
	55.8%	(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (neg.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (*.f32 cosTheta (neg.f32 cosTheta))))))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	60.2%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	98.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
▶	98.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
▶	94.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.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)))) cosTheta))
	96.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	96.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	91.7%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	96.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) 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)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
▶	98.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	91.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	60.3%	(/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c)))
▶	5.3%	(/.f32 #s(literal 1 binary32) c)
	35.4%	(-.f32 (/.f32 (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (.f32 cosTheta (neg.f32 cosTheta)))))) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))) (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))) (/.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))) (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))))
	35.2%	(.f32 (fma.f32 (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal -1 binary32) (neg.f32 c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))) (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))))
	55.8%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (neg.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (.f32 cosTheta (neg.f32 cosTheta)))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
	95.5%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	92.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.3%	(exp.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c)) #s(literal -1 binary32)))

Compiler

Compiled 2 018 to 946 computations (53.1% saved)

simplify189.0ms (1.4%)

Memory

20.7MiB live, 343.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
✓	cost-diff	160	(*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	352	(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))
✓	cost-diff	416	(/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))))
✓	cost-diff	0	(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
✓	cost-diff	0	(/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta)
✓	cost-diff	0	(fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	0	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	0	(/.f32 (fma.f32 cosTheta (-.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)))) cosTheta)
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.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)))) cosTheta))
✓	cost-diff	576	(fma.f32 cosTheta (-.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))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
✓	cost-diff	64	(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))

Rules

4 518×	`accelerator-lowering-fma.f32`
4 518×	`accelerator-lowering-fma.f64`
2 656×	`-lowering-.f32`
2 656×	`-lowering-.f64`
1 660×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	441
1	95	429
2	222	425
3	532	411
4	1141	411
5	2175	411
6	5218	411
0	8339	384

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ (+ 1 c) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta))))
1
(+ (+ 1 c) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta)))
(+ 1 c)
c
(/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta))
(* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta))))
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(exp (* cosTheta (neg cosTheta)))
(* cosTheta (neg cosTheta))
(neg cosTheta)
(* (sqrt (PI)) cosTheta)
(sqrt (PI))
(PI)
(/ 1 c)
1
c
(/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))
1
(/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta)
(+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))
cosTheta
(- (+ 1 c) (sqrt (/ 1 (PI))))
(+ 1 c)
c
(sqrt (/ 1 (PI)))
(/ 1 (PI))
(PI)
(/ 1 (+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
1
(+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))
(/ (exp (* cosTheta (neg cosTheta))) cosTheta)
(exp (* cosTheta (neg cosTheta)))
(* cosTheta (neg cosTheta))
cosTheta
(neg cosTheta)
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(/ (- (- 1 cosTheta) cosTheta) (PI))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
(PI)
(+ 1 c)
c
(/ 1 (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c)))))
1
(/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c))))
(+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI)))
(/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta)
(* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta))))
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(exp (* cosTheta (neg cosTheta)))
(* cosTheta (neg cosTheta))
(neg cosTheta)
(/ 1 (+ 1 c))
(+ 1 c)
c
(sqrt (PI))
(PI)
(* (sqrt (PI)) (/ 1 (+ 1 c)))

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

localize140.0ms (1%)

Memory

10.4MiB live, 323.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
✓	accuracy	98.7%	(/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))))
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.2%	(fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.6%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.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)))) cosTheta))
✓	accuracy	98.2%	(/.f32 (fma.f32 cosTheta (-.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)))) cosTheta)
✓	accuracy	96.9%	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
✓	accuracy	98.9%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

68.0ms

256×

valid

Compiler

Compiled 435 to 40 computations (90.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-div: 18.0ms (37.6% of total)

ival-mult: 9.0ms (18.8% of total)

ival-add: 6.0ms (12.5% of total)

ival-sqrt: 6.0ms (12.5% of total)

ival-sub: 3.0ms (6.3% of total)

ival-exp: 2.0ms (4.2% of total)

ival-pi: 1.0ms (2.1% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series68.0ms (0.5%)

Memory

-13.3MiB live, 135.5MiB allocated

Counts

21 → 360

Calls

Call 1

Inputs
#<alt (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta))>
#<alt (/ 1 (+ (+ 1 c) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta))))>
#<alt (+ (+ 1 c) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta)))>
#<alt (+ 1 c)>
#<alt (/ 1 c)>
#<alt (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))>
#<alt (/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))>
#<alt (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta)>
#<alt (- (+ 1 c) (sqrt (/ 1 (PI))))>
#<alt (/ 1 (+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))>
#<alt (+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))>
#<alt (/ (exp (* cosTheta (neg cosTheta))) cosTheta)>
#<alt (exp (* cosTheta (neg cosTheta)))>
#<alt (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c))))>
#<alt (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI)))>
#<alt (* (sqrt (PI)) (/ 1 (+ 1 c)))>
#<alt (/ 1 (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c)))))>
#<alt (* (sqrt (PI)) cosTheta)>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (sqrt (/ 1 (PI)))>
#<alt (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))>

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

Calls

90 calls:

Time	Variable		Point	Expression
9.0ms	cosTheta	@	-inf	(/ 1 (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c)))))
4.0ms	cosTheta	@	inf	(/ 1 (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c)))))
3.0ms	c	@	0	(/ 1 (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c)))))
3.0ms	cosTheta	@	-inf	(/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c))))
3.0ms	c	@	-inf	(/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))

rewrite416.0ms (3%)

Memory

-5.3MiB live, 697.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 332×	`/-lowering-/.f32`
4 332×	`/-lowering-/.f64`
3 108×	`-lowering-.f32`
3 108×	`-lowering-.f64`
2 628×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	283
1	287	271
2	2718	271
0	8418	261

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 913

Calls

Call 1

Inputs
(/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta))
(/ 1 (+ (+ 1 c) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta))))
(+ (+ 1 c) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) (* (sqrt (PI)) cosTheta)))
(+ 1 c)
(/ 1 c)
(+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))
(/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))
(/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta)
(- (+ 1 c) (sqrt (/ 1 (PI))))
(/ 1 (+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
(+ (* (/ (exp (* cosTheta (neg cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))
(/ (exp (* cosTheta (neg cosTheta))) cosTheta)
(exp (* cosTheta (neg cosTheta)))
(/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c))))
(+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI)))
(* (sqrt (PI)) (/ 1 (+ 1 c)))
(/ 1 (/ (+ (* (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (/ 1 (+ 1 c))) (sqrt (PI))) (* (sqrt (PI)) (/ 1 (+ 1 c)))))
(* (sqrt (PI)) cosTheta)
(- (- 1 cosTheta) cosTheta)
(sqrt (/ 1 (PI)))
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))

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

simplify603.0ms (4.4%)

Memory

-14.9MiB live, 697.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6 998×	`accelerator-lowering-fma.f32`
6 998×	`accelerator-lowering-fma.f64`
6 936×	`-lowering-.f32`
6 936×	`-lowering-.f64`
4 692×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1098	14758
1	3665	13897
0	8250	13269

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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

eval469.0ms (3.4%)

Memory: 16.7MiB live, 357.9MiB allocated
Compiler: Compiled 63 206 to 5 179 computations (91.8% saved)

prune398.0ms (2.9%)

Memory

14.4MiB live, 496.2MiB allocated

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	1 665	23	1 688
Fresh	17	6	23
Picked	3	2	5
Done	0	0	0
Total	1 685	31	1 716

Accuracy

100.0%

Counts

1 716 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.7%	(pow.f32 (pow.f32 (/.f32 (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	56.0%	(pow.f32 (.f32 (fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)) (fma.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal -1/2 binary32))
	95.4%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) cosTheta))
	98.5%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta)))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
	98.0%	(/.f32 (sqrt.f32 (PI.f32)) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))))
▶	98.5%	(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))) (+.f32 #s(literal 1 binary32) c)))
▶	94.8%	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
	94.9%	(/.f32 cosTheta (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
▶	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	96.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	98.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	95.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
	91.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	95.3%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (fma.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	92.1%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	91.7%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	94.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	91.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	57.1%	(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))
✓	5.3%	(/.f32 #s(literal 1 binary32) c)
▶	95.9%	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (*.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
	95.5%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
▶	92.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 454 to 837 computations (42.4% saved)

simplify416.0ms (3%)

Memory

-0.8MiB live, 518.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (*.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	cost-diff	64	(neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	64	(*.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))
✓	cost-diff	576	(fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)
✓	cost-diff	0	(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	cost-diff	0	(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	0	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	cost-diff	672	(fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (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 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	64	(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))
✓	cost-diff	256	(.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))) (+.f32 #s(literal 1 binary32) c))

Rules

13 402×	`accelerator-lowering-fma.f32`
13 402×	`accelerator-lowering-fma.f64`
3 882×	`-lowering-.f32`
3 882×	`-lowering-.f64`
3 332×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	475
1	138	475
2	400	470
3	1501	454
4	6523	446
0	8495	406

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize151.0ms (1.1%)

Memory

-8.2MiB live, 383.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.6%	(/.f32 cosTheta (fma.f32 (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	accuracy	98.3%	(.f32 (/.f32 cosTheta (fma.f32 (.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (*.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	accuracy	96.9%	(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.2%	(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.6%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
✓	accuracy	99.7%	(fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	98.3%	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	accuracy	96.9%	(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.7%	(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	98.7%	(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (fma.f32 cosTheta c cosTheta))) (+.f32 #s(literal 1 binary32) c)))

Samples

77.0ms

256×

valid

Compiler

Compiled 458 to 50 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 16.0ms (27.4% of total)

ival-div: 13.0ms (22.3% of total)

ival-add: 12.0ms (20.5% of total)

ival-sqrt: 8.0ms (13.7% of total)

ival-sub: 3.0ms (5.1% of total)

ival-neg: 3.0ms (5.1% of total)

ival-exp: 2.0ms (3.4% of total)

ival-pi: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series93.0ms (0.7%)

Memory

-7.5MiB live, 210.2MiB allocated

Counts

23 → 300

Calls

Call 1

Inputs
#<alt (* (+ (sqrt (PI)) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (neg (* cosTheta cosTheta)))) (+ (* cosTheta c) cosTheta))) (+ 1 c))>
#<alt (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (neg (* cosTheta cosTheta)))) (+ (* cosTheta c) cosTheta))>
#<alt (/ (sqrt (PI)) (* (+ (sqrt (PI)) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (neg (* cosTheta cosTheta)))) (+ (* cosTheta c) cosTheta))) (+ 1 c)))>
#<alt (sqrt (PI))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (PI)>
#<alt (+ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI))))>
#<alt (/ cosTheta (+ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))>
#<alt (- 1 (sqrt (/ 1 (PI))))>
#<alt (sqrt (/ 1 (PI)))>
#<alt (/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))>
#<alt (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))>
#<alt (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta)>
#<alt (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1)>
#<alt (+ (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))>
#<alt (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI))))))>
#<alt (neg (/ 1 (PI)))>
#<alt (* (/ cosTheta (+ (* (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI))))))) (neg (/ 1 (PI))))) (+ (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))>
#<alt (+ 1 (/ -1 (sqrt (PI))))>
#<alt (/ -1 (sqrt (PI)))>
#<alt (/ cosTheta (+ (* (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI))))))) (neg (/ 1 (PI)))))>

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

Calls

75 calls:

Time	Variable		Point	Expression
14.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
9.0ms	cosTheta	@	inf	(* (/ cosTheta (+ (* (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI))))))) (neg (/ 1 (PI))))) (+ (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))
8.0ms	cosTheta	@	-inf	(* (+ (sqrt (PI)) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (neg (* cosTheta cosTheta)))) (+ (* cosTheta c) cosTheta))) (+ 1 c))
5.0ms	cosTheta	@	inf	(/ (sqrt (PI)) (* (+ (sqrt (PI)) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (neg (* cosTheta cosTheta)))) (+ (* cosTheta c) cosTheta))) (+ 1 c)))
5.0ms	cosTheta	@	-inf	(/ (sqrt (PI)) (* (+ (sqrt (PI)) (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (neg (* cosTheta cosTheta)))) (+ (* cosTheta c) cosTheta))) (+ 1 c)))

rewrite379.0ms (2.8%)

Memory

15.8MiB live, 847.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 086×	`accelerator-lowering-fma.f32`
4 086×	`accelerator-lowering-fma.f64`
4 072×	`-lowering-.f32`
4 072×	`-lowering-.f64`
2 972×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	305
1	362	290
2	3643	282
0	8333	269

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 715

Calls

Call 1

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

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

simplify489.0ms (3.6%)

Memory

-4.7MiB live, 1 067.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 144×	`accelerator-lowering-fma.f32`
7 144×	`accelerator-lowering-fma.f64`
6 524×	`-lowering-.f32`
6 524×	`-lowering-.f64`
4 760×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1421	14758
1	4801	13520
0	8774	12856

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

Inputs
(/ 1 cosTheta)
(/ (+ 1 (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) cosTheta)
(/ (+ 1 (* cosTheta (+ (* -3/2 cosTheta) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(/ (+ 1 (* cosTheta (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))))
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 5) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))))
(+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(* c (sqrt (PI)))
(* c (+ (sqrt (PI)) (+ (* (/ 1 c) (sqrt (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))))
(* c (sqrt (PI)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)))))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(/ 1 (* cosTheta (+ 1 c)))
(/ (+ (* -1 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (* -3/2 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* cosTheta (- (* cosTheta (- (* 1/2 (/ cosTheta (+ 1 c))) (* 3/2 (/ 1 (+ 1 c))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (+ 1 c))))) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (+ 1 c))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (+ 1 c))))) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (+ 1 c))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 5) (+ 1 c))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (+ 1 c))))) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))
(* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (- (* -1 c) 1))))) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (- (* -1 c) 1))))) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))
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(* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))
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(* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))
(/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)
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(* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))
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(/ 1 c)
(/ (+ 1 (* -1 (* (/ (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) c) (sqrt (PI))))) c)
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(/ 1 c)
(* -1 (/ (- (* (/ (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) c) (sqrt (PI))) 1) c))
(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))) c) (sqrt (PI)))) c)) 1) c))
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(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- 1 (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- 1 (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (- 1 (sqrt (/ 1 (PI)))))
(* cosTheta (- (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))
(* cosTheta (- (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))
(* cosTheta (- (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))))
(* cosTheta (- 1 (sqrt (/ 1 (PI)))))
(* -1 (* cosTheta (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- 1 (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- 1 (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- 1 (sqrt (/ 1 (PI))))))))
(* cosTheta (sqrt (PI)))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2)) (sqrt (pow (PI) 3))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
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(/ 1 (- 1 (sqrt (/ 1 (PI)))))
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(* cosTheta (sqrt (PI)))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))
(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (pow cosTheta 4))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 4))
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(* -2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ (sqrt -1) (sqrt 2))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (* cosTheta (pow (sqrt 2) 2)))) (* -2 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))
(/ (- (+ (* -2 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* -1 (/ (+ (* -4 (/ (* cosTheta (* (PI) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))))) (pow (sqrt 2) 2))) (* 8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (sqrt -1) (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) 2)) (pow (sqrt 2) 3))))) (pow cosTheta 4)))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (* cosTheta (pow (sqrt 2) 2))))) (pow cosTheta 4))
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(/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* (/ 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)
(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))
(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/32 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))))))))
(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4)))))))
(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))
(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
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(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(/ 1 cosTheta)
(/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(* 1/2 (pow cosTheta 3))
(* (pow cosTheta 3) (- 1/2 (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 3) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 3) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(* 1/2 (pow cosTheta 3))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) 1/2)))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))
1
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1
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(/ (+ (* -1 (/ (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/ (- (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (pow cosTheta 2))) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -1 (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))))) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))))) (pow c 3))) (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI)))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/ 1 (* (pow c 2) cosTheta))
(/ (+ (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (* c cosTheta))) (/ 1 cosTheta)) (pow c 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)))) c)) (+ (* 2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (* c (pow cosTheta 3)))) (/ 1 (* (pow cosTheta 3) (PI))))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))

Outputs
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) cosTheta)
(/.f32 (fma.f32 (+.f32 cosTheta (*.f32 cosTheta c)) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* cosTheta (+ (* -3/2 cosTheta) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (*.f32 cosTheta #s(literal -3/2 binary32))) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* cosTheta (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))))) #s(literal 1 binary32)) cosTheta)
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))
(.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))
(fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))))
(fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))) (fma.f32 #s(literal 1/16 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32)))))))
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))
(.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))) (sqrt.f32 (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))
(fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))) (sqrt.f32 (PI.f32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c)) (*.f32 (sqrt.f32 #s(literal 2 binary32)) (+.f32 (neg.f32 c) #s(literal -1 binary32))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))))
(fma.f32 #s(literal -1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c))) (.f32 (+.f32 (neg.f32 c) #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))) (sqrt.f32 (PI.f32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c)) (*.f32 (sqrt.f32 #s(literal 2 binary32)) (+.f32 (neg.f32 c) #s(literal -1 binary32)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 5) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))))
(fma.f32 #s(literal -1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c))) (.f32 (+.f32 (neg.f32 c) #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 #s(literal 1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c))) (.f32 (+.f32 (neg.f32 c) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (+.f32 (neg.f32 c) #s(literal -1 binary32))) (sqrt.f32 (PI.f32))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) c)) (.f32 (sqrt.f32 #s(literal 2 binary32)) (+.f32 (neg.f32 c) #s(literal -1 binary32))))))))
(+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))
(fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+.f32 (sqrt.f32 (PI.f32)) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (.f32 c (+.f32 (sqrt.f32 (PI.f32)) #s(literal 0 binary32)))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+.f32 (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (.f32 c (+.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(literal 0 binary32)) (*.f32 c #s(literal 0 binary32)))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+.f32 (sqrt.f32 (PI.f32)) (fma.f32 c (+.f32 (+.f32 (sqrt.f32 (PI.f32)) #s(literal 0 binary32)) (.f32 c (+.f32 #s(literal 0 binary32) (.f32 c #s(literal 0 binary32))))) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)))
(* c (sqrt (PI)))
(*.f32 c (sqrt.f32 (PI.f32)))
(* c (+ (sqrt (PI)) (+ (* (/ 1 c) (sqrt (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))
(.f32 c (fma.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta c)))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))
(.f32 c (+.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (.f32 c c))))) (fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta c)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (.f32 c c)))) (/.f32 (sqrt.f32 (PI.f32)) c))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))))
(.f32 c (+.f32 (sqrt.f32 (PI.f32)) (+.f32 (neg.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (.f32 c c))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (.f32 c (.f32 c c))))))) (fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta c)) (+.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (.f32 c c))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (.f32 c (.f32 c c)))))) (/.f32 (sqrt.f32 (PI.f32)) c)))))
(* c (sqrt (PI)))
(*.f32 c (sqrt.f32 (PI.f32)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) c)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) c))) c)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (/.f32 (+.f32 #s(literal 0 binary32) (/.f32 #s(literal 0 binary32) c)) (neg.f32 c))) c)))
(/ 1 (* cosTheta (+ 1 c)))
(/.f32 #s(literal 1 binary32) (+.f32 cosTheta (*.f32 cosTheta c)))
(/ (+ (* -1 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c))) cosTheta)
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) c))) cosTheta)
(/ (+ (* cosTheta (- (* -3/2 (/ cosTheta (+ 1 c))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 #s(literal -3/2 binary32) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) c)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))) cosTheta)
(/ (+ (* cosTheta (- (* cosTheta (- (* 1/2 (/ cosTheta (+ 1 c))) (* 3/2 (/ 1 (+ 1 c))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 #s(literal 1/2 binary32) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) c)) (/.f32 #s(literal -3/2 binary32) (+.f32 #s(literal 1 binary32) c))) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))) cosTheta)
(* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (+ 1 c))))) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))
(fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 #s(literal -2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c))))
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(* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))
(/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)
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(+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* c (+ (* -1 (* (/ (* c (exp (neg (pow cosTheta 2)))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))
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(* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))
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(/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)
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(/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))) c)
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(/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))))) c)
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(* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))
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(* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) c))
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(* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) c))) c))
(/.f32 (neg.f32 (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta c)))) c))) (neg.f32 c))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (PI))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (sqrt (PI)))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* cosTheta (+ (* -1 (* (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) (sqrt (PI)))) (* (sqrt (PI)) (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))))))))))
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(* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))
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(+ (* -1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (* (pow (+ 1 c) 2) (pow (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))) 2)))))) (* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))))
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(*.f32 cosTheta (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (- 1 (sqrt (/ 1 (PI)))))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* -1 (* cosTheta (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- 1 (sqrt (/ 1 (PI))))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- 1 (sqrt (/ 1 (PI))))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (- 1 (sqrt (/ 1 (PI))))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2)) (sqrt (pow (PI) 3))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (neg.f32 (.f32 cosTheta (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(/ 1 (- 1 (sqrt (/ 1 (PI)))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (- 1 (sqrt (/ 1 (PI))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (/ 1 (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI)))))
(-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (- 1 (sqrt (/ 1 (PI)))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (/ 1 (- 1 (sqrt (/ 1 (PI))))))) (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI)))))
(-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/ 1 (- 1 (sqrt (/ 1 (PI)))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (- 1 (sqrt (/ 1 (PI))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) (/ 1 (- 1 (sqrt (/ 1 (PI)))))))
(-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (- 1 (sqrt (/ 1 (PI)))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (- 1 (sqrt (/ 1 (PI)))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (- 1 (sqrt (/ 1 (PI)))) 2))))) cosTheta)) (/ 1 (- 1 (sqrt (/ 1 (PI))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (fma.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 cosTheta (fma.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (neg.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (sqrt.f32 (PI.f32))))
(* 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 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))))) (fma.f32 (PI.f32) (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))))))) (neg.f32 cosTheta) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)))))) (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* 2 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (sqrt -2))))
(*.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32)))) (sqrt.f32 #s(literal -2 binary32))))
(/ (+ (* -4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2)))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (pow cosTheta 4))
(/.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (.f32 (PI.f32) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))))) cosTheta) (.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (*.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32)))
(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (pow (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2))))) 2) (pow (sqrt -2) 3)))) (* 4 (/ (* cosTheta (* (PI) (+ 1 (+ c (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ 1 (pow (sqrt -2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))))) (pow (sqrt -2) 2)))) (pow cosTheta 4))) (* 2 (* (sqrt (* cosTheta (PI))) (/ 1 (sqrt -2))))) (* 4 (/ (* (PI) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (* 1/4 (* (sqrt (/ cosTheta (PI))) (/ 1 (sqrt -2)))))) (* cosTheta (pow (sqrt -2) 2))))) (pow cosTheta 4))
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (-.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)))) 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 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (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)
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(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
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(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
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(* (pow cosTheta 4) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))))
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(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))))
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(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))))
(+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -1 binary32) cosTheta) #s(literal -1 binary32)) c)))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))))
(+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -1 binary32) cosTheta) #s(literal -1 binary32)) c)))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* -1 (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* c cosTheta)
(*.f32 cosTheta c)
(* c (+ cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c))))
(*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 c)))))
(* c (+ cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c))))
(*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 c)))))
(* c (+ cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c))))
(*.f32 c (+.f32 cosTheta (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 c)))))
(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* c cosTheta)
(*.f32 cosTheta c)
(* c (+ cosTheta (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))
(*.f32 c (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta))
(* c (+ cosTheta (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))
(*.f32 c (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta))
(* c (+ cosTheta (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))
(*.f32 c (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta))
(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))
(neg.f32 (*.f32 c (neg.f32 (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))
(neg.f32 (*.f32 c (neg.f32 (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c)))))
(neg.f32 (*.f32 c (neg.f32 (fma.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c) cosTheta))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (fma.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)) (sqrt (pow (PI) 3)))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (neg.f32 (.f32 cosTheta (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))
(+.f32 (-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))))
(-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(+ (* -1 (/ (- (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (/ 1 (* cosTheta (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3))))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))) cosTheta))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) cosTheta)) (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (*.f32 cosTheta (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) cosTheta)) cosTheta))
(/ (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI))))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
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(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
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(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
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(* -1 (* cosTheta (PI)))
(*.f32 (PI.f32) (neg.f32 cosTheta))
(* cosTheta (+ (* -1 (PI)) (* -1 (* (pow cosTheta 2) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))
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(* cosTheta (+ (* -1 (PI)) (* (pow cosTheta 2) (- (* -1 (* (pow cosTheta 2) (* (pow (PI) 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4)))) (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))
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(/ (- (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (+.f32 (fma.f32 (neg.f32 (fma.f32 #s(literal -2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 2 binary32))) (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) (.f32 c c)) (/.f32 #s(literal 2 binary32) (.f32 cosTheta c))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (.f32 c c)))))) (.f32 c c))
(/ (- (+ (* -1 (/ (+ (* -1 (/ (* (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (pow cosTheta 2))) (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -1 (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta))))) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))))) (pow c 3))) (+ (/ 1 cosTheta) (/ 1 (* (pow c 2) (* (pow cosTheta 3) (PI)))))) (+ (* -2 (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (* (+ 2 (* -2 (sqrt (/ 1 (PI))))) (+ (* -2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 2 (/ 1 cosTheta)))) (pow c 2))) (+ (/ 2 (* c cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) (* (pow c 2) cosTheta)))))) (pow c 2))
(/.f32 (-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (fma.f32 (fma.f32 #s(literal -2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 2 binary32)) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (fma.f32 (fma.f32 #s(literal -2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 2 binary32)) (neg.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))) (/.f32 (.f32 (fma.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal -1 binary32) (PI.f32))) (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta))) (.f32 cosTheta (neg.f32 cosTheta)))) (.f32 c (.f32 c c)))) (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)) (+.f32 (fma.f32 (neg.f32 (fma.f32 #s(literal -2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 2 binary32))) (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (/.f32 #s(literal 2 binary32) cosTheta)) (.f32 c c)) (/.f32 #s(literal 2 binary32) (.f32 cosTheta c))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (.f32 c c)))))) (.f32 c c))
(/ 1 (* (pow c 2) cosTheta))
(/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 c c)))
(/ (+ (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (* c cosTheta))) (/ 1 cosTheta)) (pow c 2))
(/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 c c))
(/ (+ (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 #s(literal 3 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))) (neg.f32 c)) (.f32 #s(literal 2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) c)) (*.f32 c c))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (/ 1 (* (pow cosTheta 3) (PI))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)))) c)) (+ (* 2 (/ (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (- (* (pow cosTheta 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (/ 1 (PI)))) (* c (pow cosTheta 3)))) (/ 1 (* (pow cosTheta 3) (PI))))) (+ (* -4 (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta)) (/ (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2) cosTheta))) c)) (* -2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta))) c)) (/ 1 cosTheta)) (pow c 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (+.f32 (/.f32 (fma.f32 #s(literal -2 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 #s(literal 3 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))) c) (+.f32 (fma.f32 #s(literal 2 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal -1 binary32) (PI.f32)))) (.f32 c (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 #s(literal 3 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))) (neg.f32 c)) (.f32 #s(literal 2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) c)) (*.f32 c c))

eval509.0ms (3.7%)

Memory: -82.5MiB live, 556.7MiB allocated
Compiler: Compiled 80 957 to 6 879 computations (91.5% saved)

prune272.0ms (2%)

Memory

11.0MiB live, 698.6MiB allocated

Pruning

30 alts after pruning (26 fresh and 4 done)

	Pruned	Kept	Total
New	1 909	12	1 921
Fresh	10	14	24
Picked	3	2	5
Done	0	2	2
Total	1 922	30	1 952

Accuracy

100.0%

Counts

1 952 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.4%	(pow.f32 (.f32 (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal -1/2 binary32))
▶	92.3%	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))
	91.0%	(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
	91.9%	(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (.f32 cosTheta c)))) (+.f32 #s(literal 1 binary32) c)))
✓	94.8%	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
	94.9%	(/.f32 cosTheta (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
▶	97.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c)))
	97.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	96.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	98.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	91.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	92.1%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	91.7%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 1 binary32)))
▶	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	91.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
✓	5.3%	(/.f32 #s(literal 1 binary32) c)
▶	98.4%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))) (sqrt.f32 (PI.f32)))
▶	95.5%	(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
	95.5%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	95.4%	(.f32 cosTheta (fma.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
	95.5%	(.f32 cosTheta (.f32 (+.f32 (neg.f32 (.f32 (+.f32 cosTheta (.f32 cosTheta c)) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))))) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
✓	92.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 280 to 779 computations (39.1% saved)

simplify323.0ms (2.4%)

Memory

13.0MiB live, 523.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	160	(-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))
✓	cost-diff	192	(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(*.f32 (PI.f32) (neg.f32 cosTheta))
✓	cost-diff	0	(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	cost-diff	576	(fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
✓	cost-diff	64	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) cosTheta)
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	544	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))
✓	cost-diff	0	(fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))) (sqrt.f32 (PI.f32)))
✓	cost-diff	256	(.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))

Rules

13 960×	`accelerator-lowering-fma.f32`
13 960×	`accelerator-lowering-fma.f64`
4 422×	`-lowering-.f32`
4 422×	`-lowering-.f64`
1 700×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	454
1	142	440
2	404	436
3	1348	426
4	4665	407
0	8278	378

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize219.0ms (1.6%)

Memory

-4.7MiB live, 236.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.9%	(*.f32 (PI.f32) cosTheta)
✓	accuracy	98.2%	(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	98.9%	(*.f32 (PI.f32) (neg.f32 cosTheta))
✓	accuracy	98.3%	(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	accuracy	96.9%	(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	accuracy	99.6%	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
✓	accuracy	98.2%	(/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) cosTheta)
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.7%	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))
✓	accuracy	99.7%	(/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta))
✓	accuracy	99.5%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.4%	(/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.8%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fma.f32 cosTheta c cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))) (sqrt.f32 (PI.f32)))

Samples

113.0ms

256×

valid

Compiler

Compiled 433 to 53 computations (87.8% saved)

Precisions

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

ival-mult: 40.0ms (48.7% of total)

ival-div: 16.0ms (19.5% of total)

ival-add: 11.0ms (13.4% of total)

ival-sqrt: 7.0ms (8.5% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series105.0ms (0.8%)

Memory

24.1MiB live, 60.3MiB allocated

Counts

27 → 396

Calls

Call 1

Inputs
#<alt (* (+ (* (sqrt (- (- 1 cosTheta) cosTheta)) (/ (exp (neg (* cosTheta cosTheta))) (+ (* cosTheta c) cosTheta))) (sqrt (PI))) (+ 1 c))>
#<alt (* (/ 1 (* (+ (* (sqrt (- (- 1 cosTheta) cosTheta)) (/ (exp (neg (* cosTheta cosTheta))) (+ (* cosTheta c) cosTheta))) (sqrt (PI))) (+ 1 c))) (sqrt (PI)))>
#<alt (/ 1 (* (+ (* (sqrt (- (- 1 cosTheta) cosTheta)) (/ (exp (neg (* cosTheta cosTheta))) (+ (* cosTheta c) cosTheta))) (sqrt (PI))) (+ 1 c)))>
#<alt (+ (* (sqrt (- (- 1 cosTheta) cosTheta)) (/ (exp (neg (* cosTheta cosTheta))) (+ (* cosTheta c) cosTheta))) (sqrt (PI)))>
#<alt (/ (sqrt (PI)) (/ 1 cosTheta))>
#<alt (sqrt (PI))>
#<alt (PI)>
#<alt (/ 1 cosTheta)>
#<alt (+ (+ 1 c) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta))>
#<alt (/ 1 (+ (+ 1 c) (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta)))>
#<alt (+ 1 c)>
#<alt (/ (* (sqrt (/ 1 (PI))) (- 1 cosTheta)) cosTheta)>
#<alt (+ (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI))))>
#<alt (* (* (PI) (neg cosTheta)) (+ (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))>
#<alt (* (PI) (neg cosTheta))>
#<alt (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (/ (sqrt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))) (PI))) (+ 1 c))>
#<alt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))>
#<alt (/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (/ (sqrt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))) (PI))) (+ 1 c)))>
#<alt (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta)>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (/ (exp (neg (* cosTheta cosTheta))) (+ (* cosTheta c) cosTheta))>
#<alt (sqrt (/ 1 (PI)))>
#<alt (* (sqrt (/ 1 (PI))) (- 1 cosTheta))>
#<alt (+ 1 (/ -1 (sqrt (PI))))>
#<alt (/ -1 (sqrt (PI)))>
#<alt (* (PI) cosTheta)>
#<alt (/ (sqrt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))) (PI))>

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

Calls

99 calls:

Time	Variable		Point	Expression
41.0ms	c	@	inf	(* (* (PI) (neg cosTheta)) (+ (* cosTheta (+ c (+ 1 (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))
14.0ms	cosTheta	@	0	(* (PI) (neg cosTheta))
3.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (/ (sqrt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))) (PI))) (+ 1 c)))
3.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (/ (sqrt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))) (PI))) (+ 1 c)))
3.0ms	cosTheta	@	-inf	(+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (/ (sqrt (- (* (- 1 cosTheta) (PI)) (* (PI) cosTheta))) (PI))) (+ 1 c))

rewrite475.0ms (3.5%)

Memory

-22.4MiB live, 407.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 342×	`-lowering-.f32`
4 342×	`-lowering-.f64`
3 948×	`accelerator-lowering-fma.f32`
3 948×	`accelerator-lowering-fma.f64`
3 210×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	340
1	368	315
2	3669	309
0	8175	297

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 770

Calls

Call 1

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

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

simplify582.0ms (4.2%)

Memory

47.0MiB live, 545.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 256×	`accelerator-lowering-fma.f32`
7 256×	`accelerator-lowering-fma.f64`
6 066×	`-lowering-.f32`
6 066×	`-lowering-.f64`
4 668×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1398	17295
1	4630	15602
0	8194	14817

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

Inputs
(/ 1 cosTheta)
(/ (+ 1 (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) cosTheta)
(/ (+ 1 (* cosTheta (+ (* -3/2 cosTheta) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(/ (+ 1 (* cosTheta (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))))
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 5) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))))
(+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
(* c (sqrt (PI)))
(* c (+ (sqrt (PI)) (+ (* (/ 1 c) (sqrt (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))))
(* c (sqrt (PI)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)))))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (PI))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (sqrt (PI)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* cosTheta (+ (* -1 (* (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) (sqrt (PI)))) (* (sqrt (PI)) (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))))))))))
(* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))
(+ (* -1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (* (pow (+ 1 c) 2) (pow (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))) 2)))))) (* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))))
(+ (* -1 (* (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (pow (sqrt -2) 2) (* (pow (+ 1 c) 3) (pow (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))) 3))))) (* -1/8 (* (sqrt (pow cosTheta 3)) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (* (pow (+ 1 c) 2) (pow (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))) 2))))))) (pow cosTheta 4)) (sqrt (PI)))) (+ (* -1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (* (pow (+ 1 c) 2) (pow (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))) 2)))))) (* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))))
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(/ 1 c)
(/ (+ 1 (* -1 (* (/ (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) c) (sqrt (PI))))) c)
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(/ 1 c)
(* -1 (/ (- (* (/ (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) c) (sqrt (PI))) 1) c))
(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))) c) (sqrt (PI)))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) c) (sqrt (PI)))) c))) c)) 1) c))
cosTheta
(* cosTheta (+ 1 (* -1 (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))))
(* cosTheta (+ 1 (* cosTheta (- (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))))
(* cosTheta (+ 1 (* cosTheta (- (* cosTheta (- (+ 3/2 (* -1 (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))))) (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))))
(/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))
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c
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c
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(PI)
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/8 (* (sqrt (/ 1 (pow (PI) 5))) (pow (- (* -1 (PI)) (PI)) 2)))))))) (* (PI) (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))))))))
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(* 2 (* (sqrt (/ 1 (* (pow cosTheta 7) (- (* -1 (PI)) (PI))))) (PI)))
(/ (+ (* -4 (/ (* (pow (PI) 2) (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))))) (* cosTheta (- (* -1 (PI)) (PI))))) (* 2 (* (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))) (PI)))) (pow cosTheta 4))
(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (* (pow (PI) 3) (pow (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))))) 2)))) (* 4 (/ (* cosTheta (* (pow (PI) 2) (+ 1 (+ c (+ (* -1/2 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (PI))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI))))))))) (- (* -1 (PI)) (PI))))) (pow cosTheta 4))) (* 2 (* (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))) (PI)))) (* 4 (/ (* (pow (PI) 2) (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))))) (* cosTheta (- (* -1 (PI)) (PI)))))) (pow cosTheta 4))
(/ (- (+ (* -1 (/ (+ (* -8 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (* (pow (PI) 3) (* (+ 1 (+ c (+ (* -1/2 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (PI))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI))))))) (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))))))))) (+ (* -2 (* (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))) (* (PI) (* (+ (* -8 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (* (pow (PI) 3) (pow (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))))) 2)))) (* 4 (/ (* cosTheta (* (pow (PI) 2) (+ 1 (+ c (+ (* -1/2 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (PI))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI))))))))) (- (* -1 (PI)) (PI))))) (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))))))))) (* 4 (/ (* cosTheta (* (pow (PI) 2) (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (pow (- (* -1 (PI)) (PI)) 5))) (pow (PI) 2))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (PI))) (* 1/2 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))))))) (- (* -1 (PI)) (PI)))))) (pow cosTheta 6))) (* 2 (* (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))) (PI)))) (+ (* -8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (* -1 (PI)) (PI)) 3)))) (* (pow (PI) 3) (pow (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI)))))) 2)))) (+ (* 4 (/ (* (pow (PI) 2) (+ 1 (+ c (+ (* -1/2 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (* -1 (PI)) (PI)) 3))) (PI))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))))))) (* (pow cosTheta 3) (- (* -1 (PI)) (PI))))) (* 4 (/ (* (pow (PI) 2) (+ (* -1 (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))) (* 1/4 (sqrt (/ cosTheta (- (* -1 (PI)) (PI))))))) (* cosTheta (- (* -1 (PI)) (PI)))))))) (pow cosTheta 4))
(* -2 (* (sqrt (/ 1 (* (pow cosTheta 7) (- (PI) (* -1 (PI)))))) (* (PI) (sqrt -1))))
(/ (+ (* -4 (/ (* (pow (PI) 2) (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))) (* cosTheta (- (PI) (* -1 (PI)))))) (* -2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (* (PI) (sqrt -1))))) (pow cosTheta 4))
(/ (- (+ (* -2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (* (PI) (sqrt -1)))) (* -1 (/ (+ (* -4 (/ (* cosTheta (* (pow (PI) 2) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))))))))) (- (PI) (* -1 (PI))))) (* 8 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (pow (PI) 3) (* (sqrt -1) (pow (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1)))) 2)))))) (pow cosTheta 4)))) (* 4 (/ (* (pow (PI) 2) (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))) (* cosTheta (- (PI) (* -1 (PI))))))) (pow cosTheta 4))
(/ (- (+ (* -2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (* (PI) (sqrt -1)))) (* -1 (/ (+ (* -8 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (pow (PI) 3) (* (sqrt -1) (* (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))))))) (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))))))) (+ (* -2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (* (PI) (* (sqrt -1) (* (+ (* -4 (/ (* cosTheta (* (pow (PI) 2) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))))))))) (- (PI) (* -1 (PI))))) (* 8 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (pow (PI) 3) (* (sqrt -1) (pow (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1)))) 2)))))) (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))))))) (* 4 (/ (* cosTheta (* (pow (PI) 2) (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 5))) (* (pow (PI) 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* 1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))))) (- (PI) (* -1 (PI))))))) (pow cosTheta 6)))) (+ (* -4 (/ (* (pow (PI) 2) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI))))))))) (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (+ (* 4 (/ (* (pow (PI) 2) (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))) (* cosTheta (- (PI) (* -1 (PI)))))) (* 8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 3)))) (* (pow (PI) 3) (* (sqrt -1) (pow (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1)))) 2)))))))) (pow cosTheta 4))
(/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 3)) (/ 1 (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 4))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 3)))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c (* cosTheta (PI)))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c (* cosTheta (PI)))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c (* cosTheta (PI)))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2) c) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) 2)) c)) (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))))) c)) 1) c))
(/ 1 cosTheta)
(/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(* 1/2 (pow cosTheta 3))
(* (pow cosTheta 3) (- 1/2 (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 3) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(* (pow cosTheta 3) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(* 1/2 (pow cosTheta 3))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) 1/2)))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))
1
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* -2 cosTheta)
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 1 (* cosTheta (+ 1 c)))
(/ (+ (* -1 (/ (pow cosTheta 2) (+ 1 c))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* (pow cosTheta 2) (- (* 1/2 (/ (pow cosTheta 2) (+ 1 c))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ (* -1/6 (/ (pow cosTheta 2) (+ 1 c))) (* 1/2 (/ 1 (+ 1 c))))) (/ 1 (+ 1 c)))) (/ 1 (+ 1 c))) cosTheta)
(/ (exp (neg (pow cosTheta 2))) (* cosTheta (+ 1 c)))
(/ (exp (neg (pow cosTheta 2))) (* cosTheta (+ 1 c)))
(/ (exp (neg (pow cosTheta 2))) (* cosTheta (+ 1 c)))
(/ (exp (neg (pow cosTheta 2))) (* cosTheta (+ 1 c)))
(* -1 (/ (exp (neg (pow cosTheta 2))) (* cosTheta (- (* -1 c) 1))))
(* -1 (/ (exp (neg (pow cosTheta 2))) (* cosTheta (- (* -1 c) 1))))
(* -1 (/ (exp (neg (pow cosTheta 2))) (* cosTheta (- (* -1 c) 1))))
(* -1 (/ (exp (neg (pow cosTheta 2))) (* cosTheta (- (* -1 c) 1))))
(/ (exp (neg (pow cosTheta 2))) cosTheta)
(+ (* -1 (/ (* c (exp (neg (pow cosTheta 2)))) cosTheta)) (/ (exp (neg (pow cosTheta 2))) cosTheta))
(+ (* c (- (/ (* c (exp (neg (pow cosTheta 2)))) cosTheta) (/ (exp (neg (pow cosTheta 2))) cosTheta))) (/ (exp (neg (pow cosTheta 2))) cosTheta))
(+ (* c (- (* c (- (* -1 (/ (* c (exp (neg (pow cosTheta 2)))) cosTheta)) (* -1 (/ (exp (neg (pow cosTheta 2))) cosTheta)))) (/ (exp (neg (pow cosTheta 2))) cosTheta))) (/ (exp (neg (pow cosTheta 2))) cosTheta))
(/ (exp (neg (pow cosTheta 2))) (* c cosTheta))
(/ (+ (* -1 (/ (exp (neg (pow cosTheta 2))) (* c cosTheta))) (/ (exp (neg (pow cosTheta 2))) cosTheta)) c)
(/ (- (+ (/ (exp (neg (pow cosTheta 2))) cosTheta) (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta))) (/ (exp (neg (pow cosTheta 2))) (* c cosTheta))) c)
(/ (- (+ (* -1 (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta))) (/ (exp (neg (pow cosTheta 2))) cosTheta)) (+ (* -1 (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta))) (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)))) c)
(/ (exp (neg (pow cosTheta 2))) (* c cosTheta))
(* -1 (/ (+ (* -1 (/ (exp (neg (pow cosTheta 2))) cosTheta)) (/ (exp (neg (pow cosTheta 2))) (* c cosTheta))) c))
(* -1 (/ (+ (* -1 (/ (exp (neg (pow cosTheta 2))) cosTheta)) (* -1 (/ (- (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (/ (exp (neg (pow cosTheta 2))) cosTheta)) c))) c))
(* -1 (/ (+ (* -1 (/ (exp (neg (pow cosTheta 2))) cosTheta)) (* -1 (/ (- (* -1 (/ (- (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (/ (exp (neg (pow cosTheta 2))) cosTheta)) c)) (/ (exp (neg (pow cosTheta 2))) cosTheta)) c))) c))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(* cosTheta (PI))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* 1/2 (* (* cosTheta (- (* -1 (PI)) (PI))) (sqrt (/ 1 (pow (PI) 3))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1/8 (* (* cosTheta (pow (- (* -1 (PI)) (PI)) 2)) (sqrt (/ 1 (pow (PI) 5))))) (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))) (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow (PI) 5))) (pow (- (* -1 (PI)) (PI)) 2))) (* 1/16 (* (* cosTheta (pow (- (* -1 (PI)) (PI)) 3)) (sqrt (/ 1 (pow (PI) 7))))))))))
(* (sqrt (* cosTheta (- (* -1 (PI)) (PI)))) (/ 1 (PI)))
(* cosTheta (+ (* 1/2 (sqrt (/ 1 (* (pow cosTheta 3) (- (* -1 (PI)) (PI)))))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (* -1 (PI)) (PI)) 3)))) (PI))) (+ (* 1/2 (sqrt (/ 1 (* (pow cosTheta 3) (- (* -1 (PI)) (PI)))))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (* -1 (PI)) (PI)) 3)))) (PI))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (pow (- (* -1 (PI)) (PI)) 5)))) (pow (PI) 2))) (+ (* 1/2 (sqrt (/ 1 (* (pow cosTheta 3) (- (* -1 (PI)) (PI)))))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))))))
(* -1 (* (sqrt (* cosTheta (- (PI) (* -1 (PI))))) (/ (sqrt -1) (PI))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (sqrt -1))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 3)))) (* (PI) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (sqrt -1))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 3)))) (* (PI) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (pow (- (PI) (* -1 (PI))) 5)))) (* (pow (PI) 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (sqrt -1))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI))))))))

Outputs
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) cosTheta)
(/.f32 (fma.f32 (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c)) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* cosTheta (+ (* -3/2 cosTheta) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (*.f32 cosTheta #s(literal -3/2 binary32))) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* cosTheta (+ (* cosTheta (- (* 1/2 cosTheta) 3/2)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))))) #s(literal 1 binary32)) cosTheta)
(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))
(.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))
(fma.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))))))
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(* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))
(.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (+.f32 #s(literal -1 binary32) (neg.f32 c))) (sqrt.f32 (PI.f32))))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))
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(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1)))))))
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(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 3) (- (* -1 c) 1))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (pow (sqrt 2) 5) (- (* -1 c) 1))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ 1 c))) (* (sqrt 2) (- (* -1 c) 1))))) (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) (- (* -1 c) 1))))))))
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(+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))
(fma.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
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(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
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(+ (sqrt (PI)) (+ (* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* c (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))
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(* c (sqrt (PI)))
(*.f32 c (sqrt.f32 (PI.f32)))
(* c (+ (sqrt (PI)) (+ (* (/ 1 c) (sqrt (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))
(.f32 c (fma.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta c)))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))
(.f32 c (+.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (.f32 c c))))) (fma.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (+.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta c)) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (.f32 c c)))) (/.f32 (sqrt.f32 (PI.f32)) c))))
(* c (+ (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (/ 1 c) (sqrt (PI))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 2) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))) (* (/ (exp (neg (pow cosTheta 2))) (* (pow c 3) cosTheta)) (sqrt (- 1 (* 2 cosTheta)))))))))))
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(* c (sqrt (PI)))
(*.f32 c (sqrt.f32 (PI.f32)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) c)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) c))) c)))
(* -1 (* c (+ (* -1 (sqrt (PI))) (* -1 (/ (+ (sqrt (PI)) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta)))))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 (sqrt.f32 (PI.f32))) (/.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (sqrt.f32 (PI.f32))) (/.f32 (+.f32 #s(literal 0 binary32) (/.f32 #s(literal 0 binary32) c)) (neg.f32 c))) c)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (sqrt (PI))))))
(.f32 cosTheta (.f32 (fma.f32 (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (sqrt (PI)))))))
(.f32 cosTheta (fma.f32 (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 cosTheta (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 3/2 binary32) (.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c)))))) (* cosTheta (+ (* -1 (* (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))) (sqrt (PI)))) (* (sqrt (PI)) (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))))))))))
(.f32 cosTheta (fma.f32 (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 cosTheta (.f32 (sqrt.f32 (PI.f32)) (fma.f32 (fma.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 3/2 binary32) (.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))))) (.f32 #s(literal 3/2 binary32) (+.f32 #s(literal 1 binary32) c))) #s(literal 1/2 binary32)) (neg.f32 cosTheta) (+.f32 #s(literal 3/2 binary32) (.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))))))))))))
(* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))))))
(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (/.f32 (.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32)))))
(+ (* -1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (* (pow (+ 1 c) 2) (pow (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c)))) 2)))))) (* (sqrt (PI)) (/ 1 (* (+ 1 c) (+ (sqrt (PI)) (* (sqrt (/ 1 cosTheta)) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -2)) (+ 1 c))))))))
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(/.f32 #s(literal 1 binary32) c)
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(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))) c) (sqrt (PI)))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* -1 (/ (+ (* -1 (* (sqrt (PI)) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))))) (* (/ (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (PI)) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta)))))))) (+ (* (sqrt (/ 1 (PI))) (* (+ (sqrt (/ 1 (PI))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))) (+ (* -1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))) (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (- 1 (* 2 cosTheta))))))) (* (/ (exp (neg (pow cosTheta 2))) (* cosTheta (PI))) (sqrt (- 1 (* 2 cosTheta))))))) c) (sqrt (PI)))) c))) c)) 1) c))
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cosTheta
(* cosTheta (+ 1 (* -1 (* cosTheta (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))))
(.f32 cosTheta (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (neg.f32 cosTheta) #s(literal 1 binary32)))
(* cosTheta (+ 1 (* cosTheta (- (* cosTheta (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))))
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(* cosTheta (+ 1 (* cosTheta (- (* cosTheta (- (+ 3/2 (* -1 (* cosTheta (+ 1/2 (+ (* 3/2 (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))) (* (+ 1 c) (* (- 3/2 (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2)))) (- (sqrt (PI)) (/ 1 (+ 1 c)))))))))) (* -1 (* (pow (+ 1 c) 2) (pow (- (sqrt (PI)) (/ 1 (+ 1 c))) 2))))) (* (+ 1 c) (- (sqrt (PI)) (/ 1 (+ 1 c))))))))
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 3) c) (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2)) c)) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))) c) (*.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (fma.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (neg.f32 cosTheta) (.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (PI.f32)))) (sqrt.f32 (PI.f32))))
(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
(+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
(-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))
(+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (-.f32 (/.f32 #s(literal 1 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))) (.f32 cosTheta (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (+.f32 (neg.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 cosTheta (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta))
1
#s(literal 1 binary32)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
c
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
c
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))))
(+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))))
(+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))))
(+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c)))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* -1 (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(* -1 (* cosTheta (+ (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(*.f32 (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 cosTheta))
(+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (sqrt (/ 1 (PI)))) (+ (* c cosTheta) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* c cosTheta)
(*.f32 cosTheta c)
(* c (+ cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c))))
(.f32 c (+.f32 (-.f32 cosTheta (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)) (/.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* c (+ cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c))))
(.f32 c (+.f32 (-.f32 cosTheta (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)) (/.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* c (+ cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))) c))))
(.f32 c (+.f32 (-.f32 cosTheta (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)) (/.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) c)))))
(*.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) c)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* (pow cosTheta 4) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (* 1/4 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1)))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI))))) (pow cosTheta 4))) (+ (* -1 (/ (+ (* 1/32 (* (sqrt (/ (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 5))) (* (pow (PI) 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (pow (- (PI) (* -1 (PI))) 3))) (* (PI) (sqrt -1)))) (* 1/2 (* (sqrt (/ cosTheta (- (PI) (* -1 (PI))))) (sqrt -1))))) (pow cosTheta 6))) (+ (* -1/2 (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))) (+ (/ 1 (pow cosTheta 4)) (/ c (pow cosTheta 4))))))))
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(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))))
(fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) c))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))))
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(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))))
(+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) c))
c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c (* cosTheta (PI)))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c (* cosTheta (PI)))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c (* cosTheta (PI)))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI))))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) c)) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (*.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) c)) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (*.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* cosTheta (PI))) (sqrt (- (* (PI) (- 1 cosTheta)) (* cosTheta (PI)))))) c)) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (*.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)) (neg.f32 c)) #s(literal -1 binary32)))
(PI)
(PI.f32)
(+ (PI) (* cosTheta (- (* -1 (PI)) (PI))))
(fma.f32 cosTheta (*.f32 (PI.f32) #s(literal -2 binary32)) (PI.f32))
(+ (PI) (* cosTheta (- (* -1 (PI)) (PI))))
(fma.f32 cosTheta (*.f32 (PI.f32) #s(literal -2 binary32)) (PI.f32))
(+ (PI) (* cosTheta (- (* -1 (PI)) (PI))))
(fma.f32 cosTheta (*.f32 (PI.f32) #s(literal -2 binary32)) (PI.f32))
(* cosTheta (- (* -1 (PI)) (PI)))
(.f32 cosTheta (.f32 (PI.f32) #s(literal -2 binary32)))
(* cosTheta (- (+ (* -1 (PI)) (/ (PI) cosTheta)) (PI)))
(*.f32 cosTheta (-.f32 (-.f32 (/.f32 (PI.f32) cosTheta) (PI.f32)) (PI.f32)))
(* cosTheta (- (+ (* -1 (PI)) (/ (PI) cosTheta)) (PI)))
(*.f32 cosTheta (-.f32 (-.f32 (/.f32 (PI.f32) cosTheta) (PI.f32)) (PI.f32)))
(* cosTheta (- (+ (* -1 (PI)) (/ (PI) cosTheta)) (PI)))
(*.f32 cosTheta (-.f32 (-.f32 (/.f32 (PI.f32) cosTheta) (PI.f32)) (PI.f32)))
(* -1 (* cosTheta (- (PI) (* -1 (PI)))))
(.f32 cosTheta (.f32 (PI.f32) #s(literal -2 binary32)))
(* -1 (* cosTheta (- (+ (PI) (* -1 (/ (PI) cosTheta))) (* -1 (PI)))))
(*.f32 (neg.f32 cosTheta) (+.f32 (PI.f32) (-.f32 (PI.f32) (/.f32 (PI.f32) cosTheta))))
(* -1 (* cosTheta (- (+ (PI) (* -1 (/ (PI) cosTheta))) (* -1 (PI)))))
(*.f32 (neg.f32 cosTheta) (+.f32 (PI.f32) (-.f32 (PI.f32) (/.f32 (PI.f32) cosTheta))))
(* -1 (* cosTheta (- (+ (PI) (* -1 (/ (PI) cosTheta))) (* -1 (PI)))))
(*.f32 (neg.f32 cosTheta) (+.f32 (PI.f32) (-.f32 (PI.f32) (/.f32 (PI.f32) cosTheta))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))))))))
(.f32 cosTheta (fma.f32 (neg.f32 (.f32 cosTheta (PI.f32))) (+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) #s(literal -2 binary32))) c)) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/8 (* (sqrt (/ 1 (pow (PI) 5))) (pow (- (* -1 (PI)) (PI)) 2)))))))) (* (PI) (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))))))))
(.f32 cosTheta (fma.f32 cosTheta (neg.f32 (fma.f32 cosTheta (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) #s(literal -2 binary32))) c)) (+.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) #s(literal -2 binary32))) c))) (neg.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (fma.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (.f32 (PI.f32) #s(literal -2 binary32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (+.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) #s(literal -2 binary32))) c))))) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/8 (* (sqrt (/ 1 (pow (PI) 5))) (pow (- (* -1 (PI)) (PI)) 2))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/8 (* (sqrt (/ 1 (pow (PI) 5))) (pow (- (* -1 (PI)) (PI)) 2))))))) (* (PI) (+ (* -1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))) (* 1/16 (* (sqrt (/ 1 (pow (PI) 7))) (pow (- (* -1 (PI)) (PI)) 3))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/8 (* (sqrt (/ 1 (pow (PI) 5))) (pow (- (* -1 (PI)) (PI)) 2)))))))) (* (PI) (+ 1 (+ c (* 1/2 (* (sqrt (/ 1 (pow (PI) 3))) (- (* -1 (PI)) (PI)))))))))))
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(* 2 (* (sqrt (/ 1 (* (pow cosTheta 7) (- (* -1 (PI)) (PI))))) (PI)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (.f32 (PI.f32) #s(literal -2 binary32)))))))
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(.f32 cosTheta (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal -2 binary32))))) (/.f32 (sqrt.f32 (/.f32 (.f32 (PI.f32) #s(literal -2 binary32)) cosTheta)) (PI.f32))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (* -1 (PI)) (PI)) 3)))) (PI))) (+ (* 1/2 (sqrt (/ 1 (* (pow cosTheta 3) (- (* -1 (PI)) (PI)))))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI))))))
(.f32 cosTheta (fma.f32 #s(literal -1/8 binary32) (.f32 (PI.f32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (.f32 (PI.f32) #s(literal -2 binary32)))))))) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal -2 binary32))))) (/.f32 (sqrt.f32 (/.f32 (*.f32 (PI.f32) #s(literal -2 binary32)) cosTheta)) (PI.f32)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (* -1 (PI)) (PI)) 3)))) (PI))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (pow (- (* -1 (PI)) (PI)) 5)))) (pow (PI) 2))) (+ (* 1/2 (sqrt (/ 1 (* (pow cosTheta 3) (- (* -1 (PI)) (PI)))))) (* (sqrt (/ (- (* -1 (PI)) (PI)) cosTheta)) (/ 1 (PI)))))))
(.f32 cosTheta (fma.f32 #s(literal -1/8 binary32) (.f32 (PI.f32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (.f32 (PI.f32) #s(literal -2 binary32)))))))) (fma.f32 #s(literal 1/16 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (pow.f32 (.f32 (PI.f32) #s(literal -2 binary32)) #s(literal 5 binary32)))))) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal -2 binary32))))) (/.f32 (sqrt.f32 (/.f32 (*.f32 (PI.f32) #s(literal -2 binary32)) cosTheta)) (PI.f32))))))
(* -1 (* (sqrt (* cosTheta (- (PI) (* -1 (PI))))) (/ (sqrt -1) (PI))))
(/.f32 (.f32 (sqrt.f32 (.f32 cosTheta (+.f32 (PI.f32) (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (PI.f32)))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (sqrt -1))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI))))))
(.f32 (neg.f32 cosTheta) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (+.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 #s(literal -1 binary32)) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (PI.f32)) (sqrt.f32 (/.f32 (+.f32 (PI.f32) (PI.f32)) cosTheta)))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 3)))) (* (PI) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (sqrt -1))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI)))))))
(neg.f32 (.f32 cosTheta (fma.f32 #s(literal -1/8 binary32) (.f32 (.f32 (PI.f32) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (.f32 (+.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 (PI.f32) (PI.f32)) (+.f32 (PI.f32) (PI.f32)))))))) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (+.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 #s(literal -1 binary32)) (*.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (PI.f32)) (sqrt.f32 (/.f32 (+.f32 (PI.f32) (PI.f32)) cosTheta)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (pow (- (PI) (* -1 (PI))) 3)))) (* (PI) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (pow (- (PI) (* -1 (PI))) 5)))) (* (pow (PI) 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (- (PI) (* -1 (PI)))))) (sqrt -1))) (* (sqrt (/ (- (PI) (* -1 (PI))) cosTheta)) (/ (sqrt -1) (PI))))))))
(neg.f32 (.f32 cosTheta (fma.f32 #s(literal -1/8 binary32) (.f32 (.f32 (PI.f32) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (.f32 (+.f32 (PI.f32) (PI.f32)) (.f32 (+.f32 (PI.f32) (PI.f32)) (+.f32 (PI.f32) (PI.f32)))))))) (fma.f32 #s(literal 1/16 binary32) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (PI.f32) (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (pow.f32 (+.f32 (PI.f32) (PI.f32)) #s(literal 5 binary32)))))) (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (+.f32 (PI.f32) (PI.f32)))))) (sqrt.f32 #s(literal -1 binary32)) (*.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (PI.f32)) (sqrt.f32 (/.f32 (+.f32 (PI.f32) (PI.f32)) cosTheta))))))))

eval230.0ms (1.7%)

Memory: 12.1MiB live, 483.6MiB allocated
Compiler: Compiled 60 664 to 6 258 computations (89.7% saved)

prune305.0ms (2.2%)

Memory

-29.8MiB live, 691.9MiB allocated

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	1 700	19	1 719
Fresh	9	12	21
Picked	4	1	5
Done	0	4	4
Total	1 713	36	1 749

Accuracy

100.0%

Counts

1 749 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	92.3%	(/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))
	91.0%	(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
✓	94.8%	(/.f32 cosTheta (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)))
	97.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	96.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	94.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c)))
	95.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	94.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
	97.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	98.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
	92.3%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 1 binary32)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) c))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	95.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) c)))
	94.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
✓	5.3%	(/.f32 #s(literal 1 binary32) c)
	92.3%	(*.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
	55.3%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 (.f32 (.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (sqrt.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))))) (.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (sqrt.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))))) (.f32 cosTheta (.f32 (PI.f32) (.f32 cosTheta (PI.f32))))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)))) (.f32 cosTheta (PI.f32))) (neg.f32 (+.f32 #s(literal 1 binary32) c))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (/.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal 1 binary32) c))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))) (sqrt.f32 (PI.f32)))
	95.5%	(.f32 (.f32 (fma.f32 cosTheta (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (PI.f32))
	95.5%	(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
	95.2%	(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c))))
	92.6%	(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
	95.5%	(.f32 (.f32 cosTheta (fma.f32 (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (neg.f32 cosTheta) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
	95.4%	(.f32 cosTheta (fma.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
✓	92.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 3 077 to 875 computations (71.6% saved)

regimes136.0ms (1%)

Memory

0.4MiB live, 366.9MiB allocated

Counts

83 → 1

Calls

Call 1

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

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

Calls

6 calls:

23.0ms	cosTheta
23.0ms	(+.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))))
23.0ms	(.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)))
23.0ms	c
22.0ms	(/.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
98.6%	1	`cosTheta`
98.6%	1	`c`
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	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes98.0ms (0.7%)

Memory

-3.5MiB live, 233.1MiB allocated

Counts

58 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

17.0ms	c
17.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
16.0ms	(.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)))
16.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
16.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta`
98.2%	1	`c`
98.2%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.2%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.2%	1	`(+.f32 #s(literal 1 binary32) c)`
98.2%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes119.0ms (0.9%)

Memory

28.1MiB live, 231.1MiB allocated

Counts

53 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))
(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(*.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) c))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
(.f32 cosTheta (fma.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 #s(literal 1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (+.f32 cosTheta (*.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) c))))
(/.f32 (sqrt.f32 (PI.f32)) (.f32 (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (.f32 cosTheta c)))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(.f32 (.f32 cosTheta (fma.f32 (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c)))) (neg.f32 cosTheta) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(.f32 cosTheta (.f32 (+.f32 (neg.f32 (.f32 (+.f32 cosTheta (.f32 cosTheta c)) (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))))) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (fma.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(/.f32 cosTheta (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(.f32 (.f32 (PI.f32) (neg.f32 cosTheta)) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
(.f32 (.f32 (fma.f32 cosTheta (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta)) (PI.f32))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta c cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.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)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 cosTheta (PI.f32))) (sqrt.f32 (.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) c) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) 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)) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) cosTheta))) (PI.f32)) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (fma.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) c))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)) (/.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal 1 binary32) c))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))

Outputs

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

Calls

6 calls:

31.0ms	(.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)))
26.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
18.0ms	cosTheta
15.0ms	c
15.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes130.0ms (0.9%)

Memory

-24.1MiB live, 172.7MiB allocated

Counts

42 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

48.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
25.0ms	c
22.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
12.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
11.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes124.0ms (0.9%)

Memory

4.8MiB live, 125.9MiB allocated

Counts

38 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

43.0ms	(+.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))))
29.0ms	cosTheta
19.0ms	(+.f32 #s(literal 1 binary32) c)
11.0ms	c
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
97.5%	1	`c`
97.5%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.5%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.5%	1	`(+.f32 #s(literal 1 binary32) c)`
97.5%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes81.0ms (0.6%)

Memory

24.6MiB live, 140.8MiB allocated

Counts

35 → 1

Calls

Call 1

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

Calls

6 calls:

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)))
19.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
11.0ms	c
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.3%	1	`cosTheta`
97.3%	1	`c`
97.3%	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)))))`
97.3%	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))))`
97.3%	1	`(+.f32 #s(literal 1 binary32) c)`
97.3%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes147.0ms (1.1%)

Memory

-31.1MiB live, 125.7MiB allocated

Counts

33 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

42.0ms	(.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)))
29.0ms	(/.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)))))
26.0ms	(+.f32 #s(literal 1 binary32) c)
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))))

Results

Accuracy	Segments	Branch
96.8%	1	`cosTheta`
96.8%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.8%	1	`c`
96.8%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes98.0ms (0.7%)

Memory

-16.9MiB live, 129.1MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

37.0ms	(+.f32 #s(literal 1 binary32) c)
22.0ms	cosTheta
11.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	c

Results

Accuracy	Segments	Branch
95.6%	1	`cosTheta`
95.6%	1	`c`
95.6%	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)))))`
95.6%	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))))`
95.6%	1	`(+.f32 #s(literal 1 binary32) c)`
95.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes88.0ms (0.6%)

Memory

20.5MiB live, 101.4MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

33.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
27.0ms	c
7.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
7.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.5%	1	`cosTheta`
95.5%	1	`c`
95.5%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.5%	1	`(+.f32 #s(literal 1 binary32) c)`
95.5%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.5%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes114.0ms (0.8%)

Memory

-5.6MiB live, 112.1MiB allocated

Counts

23 → 1

Calls

Call 1

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

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

Calls

6 calls:

46.0ms	(+.f32 #s(literal 1 binary32) c)
25.0ms	c
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)))
7.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
7.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
95.5%	1	`cosTheta`
95.5%	1	`c`
95.5%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.5%	1	`(+.f32 #s(literal 1 binary32) c)`
95.5%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.5%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes76.0ms (0.5%)

Memory

3.5MiB live, 82.7MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

6 calls:

32.0ms	(+.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))))
25.0ms	cosTheta
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)))))
5.0ms	c
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)))

Results

Accuracy	Segments	Branch
95.4%	1	`c`
95.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.4%	1	`(+.f32 #s(literal 1 binary32) c)`
95.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
95.4%	1	`cosTheta`
95.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes42.0ms (0.3%)

Memory

-9.2MiB live, 70.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

25.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	c
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 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	cosTheta

Results

Accuracy	Segments	Branch
92.6%	1	`cosTheta`
92.6%	1	`c`
92.6%	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)))))`
92.6%	1	`(+.f32 #s(literal 1 binary32) c)`
92.6%	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))))`
92.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes13.0ms (0.1%)

Memory

9.1MiB live, 51.7MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

6 calls:

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)))))
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
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
92.5%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
92.5%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
92.5%	1	`cosTheta`
92.5%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
92.5%	1	`c`
92.5%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes9.0ms (0.1%)

Memory

-9.9MiB live, 29.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
5.3%	1	`c`
5.3%	1	`cosTheta`
5.3%	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)))))`
5.3%	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))))`
5.3%	1	`(+.f32 #s(literal 1 binary32) c)`
5.3%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

simplify81.0ms (0.6%)

Memory

11.4MiB live, 50.1MiB allocated

Algorithm

1×	egg-herbie

Rules

546×	`distribute-lft-neg-in_binary32`
312×	`unsub-neg_binary32`
270×	`neg-mul-1_binary32`
266×	`neg-sub0_binary32`
236×	`cancel-sign-sub_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	282
1	123	282
2	149	280
3	182	280
4	228	280
5	312	280
6	426	280
7	586	280
8	831	280
9	1009	280
10	1129	280
11	1202	280
12	1256	280
13	1315	280
14	1388	280
15	1471	280
16	1537	280
17	1611	280
18	1664	280
19	1692	280
20	1698	280
21	1698	280

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.6s (11.5%)

Memory

18.1MiB live, 1 713.8MiB allocated

Rules

9 656×	`accelerator-lowering-fma.f32`
9 656×	`accelerator-lowering-fma.f64`
7 256×	`accelerator-lowering-fma.f32`
7 256×	`accelerator-lowering-fma.f64`
7 144×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1098	14758
1	3665	13897
0	8250	13269
0	1421	14758
1	4801	13520
0	8774	12856
0	51	340
1	368	315
2	3669	309
0	8175	297
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311
0	1398	17295
1	4630	15602
0	8194	14817
0	38	283
1	287	271
2	2718	271
0	8418	261
0	48	305
1	362	290
2	3643	282
0	8333	269
0	18	89
1	126	80
2	1045	73
0	8542	73

Stop Event

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

Compiler

Compiled 758 to 385 computations (49.2% saved)

preprocess72.0ms (0.5%)

Memory: -12.0MiB live, 144.0MiB allocated
Compiler: Compiled 618 to 196 computations (68.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze25.0ms (0.2%)

sample2.0s (14.5%)

preprocess239.0ms (1.7%)

explain274.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify166.0ms (1.2%)

localize113.0ms (0.8%)

series24.0ms (0.2%)

rewrite381.0ms (2.8%)

simplify431.0ms (3.1%)

eval120.0ms (0.9%)

prune156.0ms (1.1%)

simplify189.0ms (1.4%)

localize140.0ms (1%)

series68.0ms (0.5%)

rewrite416.0ms (3%)

simplify603.0ms (4.4%)

eval469.0ms (3.4%)

prune398.0ms (2.9%)

simplify416.0ms (3%)

localize151.0ms (1.1%)

series93.0ms (0.7%)

rewrite379.0ms (2.8%)

simplify489.0ms (3.6%)

eval509.0ms (3.7%)

prune272.0ms (2%)

simplify323.0ms (2.4%)

localize219.0ms (1.6%)

series105.0ms (0.8%)

rewrite475.0ms (3.5%)

simplify582.0ms (4.2%)

eval230.0ms (1.7%)

prune305.0ms (2.2%)

regimes136.0ms (1%)

regimes98.0ms (0.7%)

regimes119.0ms (0.9%)

regimes130.0ms (0.9%)

regimes124.0ms (0.9%)

regimes81.0ms (0.6%)

regimes147.0ms (1.1%)

regimes98.0ms (0.7%)

regimes88.0ms (0.6%)

regimes114.0ms (0.8%)

regimes76.0ms (0.5%)

regimes42.0ms (0.3%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

simplify81.0ms (0.6%)

soundness1.6s (11.5%)

preprocess72.0ms (0.5%)

end0.0ms (0%)

Profiling