Metrics for Beckmann Sample, normalization factor

analyze27.0ms (0.2%)

Memory

7.2MiB live, 44.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.0s (15.5%)

Memory

-53.4MiB live, 2 907.6MiB allocated

Samples

1.5s	8 256×	0	valid
8.0ms	54×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 998.0ms

ival-div: 166.0ms (16.6% of total)

ival-mult: 136.0ms (13.6% of total)

const: 125.0ms (12.5% of total)

ival-sqrt: 121.0ms (12.1% of total)

ival-<: 109.0ms (10.9% of total)

ival-add: 86.0ms (8.6% of total)

ival-sub: 77.0ms (7.7% of total)

ival-exp: 70.0ms (7% of total)

ival-neg: 39.0ms (3.9% of total)

ival-pi: 30.0ms (3% of total)

ival-and: 20.0ms (2% of total)

exact: 14.0ms (1.4% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

preprocess360.0ms (2.8%)

Memory

-19.4MiB live, 232.1MiB 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 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta #s(literal 0 binary32))) (+.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)))))))

explain312.0ms (2.5%)

Memory

-11.1MiB live, 537.6MiB 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

111.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 12.0ms (23.7% of total)

ival-div: 9.0ms (17.8% of total)

ival-sqrt: 9.0ms (17.8% of total)

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

ival-exp: 4.0ms (7.9% of total)

ival-sub: 4.0ms (7.9% of total)

ival-neg: 4.0ms (7.9% of total)

ival-pi: 2.0ms (3.9% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.6MiB live, 2.6MiB 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)

simplify174.0ms (1.4%)

Memory

8.1MiB live, 212.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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	32	(.f32 (.f32 (/.f32 #s(literal 1 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	32	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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	320	(*.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 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta #s(literal 0 binary32))) (+.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 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta #s(literal 0 binary32))) (+.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))) (fma.f32 (exp.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta #s(literal 0 binary32)) #s(literal 0 binary32)))
(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
(/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta #s(literal 0 binary32)))
(/ 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 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32)))
(* (neg cosTheta) cosTheta)
(fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))
(neg cosTheta)
(neg.f32 cosTheta)

localize53.0ms (0.4%)

Memory

10.3MiB live, 127.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(-.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

31.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

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

ival-div: 5.0ms (23.5% of total)

ival-mult: 4.0ms (18.8% of total)

ival-sqrt: 3.0ms (14.1% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

12.3MiB live, 53.1MiB allocated

Counts

6 → 84

Calls

Call 1

Inputs
#<alt (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))>
#<alt (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg 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 (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 (* (/ (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 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>
#<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
3.0ms	cosTheta	@	inf	(+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))
3.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
3.0ms	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))

rewrite318.0ms (2.5%)

Memory

-6.2MiB live, 705.8MiB 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	8540	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 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg 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 (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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simplify456.0ms (3.6%)

Memory

1.8MiB live, 854.8MiB 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	4769	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 (* (/ (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 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
(+ 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 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -1/2 binary32) #s(literal -1/2 binary32))) (*.f32 cosTheta cosTheta))) 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (.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)))))
(+ (* -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 (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)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (.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))))))
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c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.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))))
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(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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c
(* -1 (* 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 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #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)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
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(* (/ 1 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 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (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)))))
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(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
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(+ 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)))))))
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(+ 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))))))))
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(+ 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)))))))))
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(* (/ 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 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) 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 #s(literal 0 binary32) (.f32 cosTheta 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))))
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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)))))))))))
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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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(* 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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(-.f32 (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 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)))) (/.f32 (fma.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))) (/.f32 (.f32 (.f32 #s(literal 1/4 binary32) cosTheta) (exp.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32)))) (.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32)) (.f32 (PI.f32) #s(literal 2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (exp.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32))) (.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal 2 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32)))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32))) (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) #s(literal 1/8 binary32)) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal 2 binary32)))))))) (/.f32 (fma.f32 #s(literal 1/16 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (exp.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32)))) (.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32)) (.f32 (PI.f32) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 4 binary32))))) (fma.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (fma.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))) (/.f32 (.f32 (.f32 #s(literal 1/4 binary32) cosTheta) (exp.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -2 binary32)))) (.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 3 binary32)) (.f32 (PI.f32) #s(literal 2 binary32)))))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c))))) (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (.f32 #s(literal -1/16 binary32) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))))) (.f32 (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))))) (+.f32 #s(literal 1 binary32) c)) #s(literal 2 binary32)))))) (pow.f32 cosTheta #s(literal 6 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))

eval68.0ms (0.5%)

Memory: 1.0MiB live, 153.8MiB allocated
Compiler: Compiled 23 777 to 2 836 computations (88.1% saved)

prune98.0ms (0.8%)

Memory

-18.7MiB live, 259.0MiB 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
	97.9%	(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 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	55.5%	(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) (-.f32 (.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 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
▶	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	98.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
	55.1%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	98.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c (.f32 c c) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (fma.f32 c (+.f32 c #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.f32 (fma.f32 c (+.f32 c #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	98.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	98.3%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	96.1%	(/.f32 #s(literal 1 binary32) (/.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)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
▶	94.6%	(/.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))
	96.7%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (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))
	92.6%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	96.7%	(/.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 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) cosTheta)))
	96.1%	(/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) cosTheta)))
	94.5%	(/.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)))
	92.3%	(/.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)) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))))))
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))))
▶	5.2%	(/.f32 #s(literal 1 binary32) c)
	95.1%	(*.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))))
	93.2%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.4%	(exp.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta) c)) #s(literal -1 binary32)))

Compiler

Compiled 1 434 to 888 computations (38.1% saved)

simplify264.0ms (2.1%)

Memory

6.6MiB live, 322.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	32	(.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	32	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	160	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta)
✓	cost-diff	0	(fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta 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 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	32	(-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))
✓	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 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	32	(.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	32	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Rules

6 916×	`accelerator-lowering-fma.f32`
6 916×	`accelerator-lowering-fma.f64`
2 880×	`-lowering-.f32`
2 880×	`-lowering-.f64`
1 258×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	394
1	91	394
2	193	384
3	381	381
4	794	381
5	1708	381
6	4157	381
7	6756	381
8	7555	381
0	8241	357

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
1
(+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))
(+ 1 c)
c
(* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))
(/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta))
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(* (sqrt (PI)) cosTheta)
(sqrt (PI))
(PI)
(exp (* (neg cosTheta) cosTheta))
(* (neg cosTheta) cosTheta)
(neg cosTheta)
(/ 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 (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
1
(+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))
(/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)
(exp (- 0 (* cosTheta cosTheta)))
(- 0 (* cosTheta cosTheta))
0
(* cosTheta cosTheta)
cosTheta
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(/ (- (- 1 cosTheta) cosTheta) (PI))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
(PI)
(+ 1 c)
c
(/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))))
1
(+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))
(+ 1 c)
c
(* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))
(/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI)))
(/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(sqrt (PI))
(PI)
(exp (* (neg cosTheta) cosTheta))
(* (neg cosTheta) cosTheta)
(neg cosTheta)

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

localize146.0ms (1.2%)

Memory

-4.8MiB live, 230.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
✓	accuracy	99.8%	(-.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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.7%	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.3%	(fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.5%	(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	97.0%	(-.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	99.8%	(-.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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	99.0%	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	accuracy	98.8%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

72.0ms

256×

valid

Compiler

Compiled 396 to 42 computations (89.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-div: 20.0ms (36.7% of total)

ival-mult: 9.0ms (16.5% of total)

ival-sqrt: 9.0ms (16.5% of total)

ival-add: 6.0ms (11% of total)

ival-exp: 4.0ms (7.3% of total)

ival-sub: 4.0ms (7.3% of total)

ival-pi: 1.0ms (1.8% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series43.0ms (0.3%)

Memory

19.9MiB live, 95.9MiB allocated

Counts

22 → 360

Calls

Call 1

Inputs
#<alt (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))>
#<alt (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))>
#<alt (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) 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 (- 0 (* cosTheta cosTheta))>
#<alt (/ 1 (+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))>
#<alt (+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))>
#<alt (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)>
#<alt (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI)))>
#<alt (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))>
#<alt (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))>
#<alt (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))))>
#<alt (* (sqrt (PI)) cosTheta)>
#<alt (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta))>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (sqrt (/ 1 (PI)))>
#<alt (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))>

Outputs
#<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)))))))>
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#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
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#<alt (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))>
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#<alt (/ 1 c)>
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#<alt (/ 1 c)>
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#<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 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)>
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#<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)))>
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#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))>
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#<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))))>
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#<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))))>
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#<alt (* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))>
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#<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
6.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
4.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
3.0ms	cosTheta	@	0	(/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta)
2.0ms	cosTheta	@	inf	(/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))
1.0ms	c	@	inf	(/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))

rewrite530.0ms (4.2%)

Memory

23.9MiB live, 1 011.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 936×	`accelerator-lowering-fma.f32`
4 936×	`accelerator-lowering-fma.f64`
4 714×	`/-lowering-/.f32`
4 714×	`/-lowering-/.f64`
4 140×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	275
1	285	257
2	2345	257
0	9560	254

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1 393

Calls

Call 1

Inputs
(+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))
(* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))
(/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(+ 1 c)
(/ 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))))
(- 0 (* cosTheta cosTheta))
(/ 1 (+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
(+ (* (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))
(/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)
(/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI)))
(+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))
(* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))
(/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))))
(* (sqrt (PI)) cosTheta)
(/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta))
(- (- 1 cosTheta) cosTheta)
(sqrt (/ 1 (PI)))
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))

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

simplify637.0ms (5%)

Memory

-2.4MiB live, 784.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 482×	`accelerator-lowering-fma.f32`
7 482×	`accelerator-lowering-fma.f64`
6 266×	`-lowering-.f32`
6 266×	`-lowering-.f64`
3 478×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	852	12606
1	2924	12025
0	8112	11532

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

eval209.0ms (1.6%)

Memory: 30.2MiB live, 415.8MiB allocated
Compiler: Compiled 73 973 to 4 748 computations (93.6% saved)

prune242.0ms (1.9%)

Memory

14.0MiB live, 400.6MiB allocated

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	1 994	18	2 012
Fresh	12	11	23
Picked	4	1	5
Done	0	0	0
Total	2 010	30	2 040

Accuracy

100.0%

Counts

2 040 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(pow.f32 (pow.f32 (fma.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.2%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) cosTheta))
▶	94.3%	(/.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)))))
	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)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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)))
	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)))
▶	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
▶	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	94.8%	(/.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)))
	96.1%	(/.f32 #s(literal 1 binary32) (/.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)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	95.4%	(/.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))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	94.7%	(/.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))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) cosTheta))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 c (+.f32 cosTheta (fma.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 cosTheta c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)))) cosTheta))
	92.6%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	94.5%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
	96.7%	(/.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 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) cosTheta)))
	94.5%	(/.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)))
	92.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))))
	52.9%	(/.f32 #s(literal 1 binary32) (.f32 c (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c))) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
▶	52.9%	(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) #s(literal -1 binary32)))))
✓	5.2%	(/.f32 #s(literal 1 binary32) c)
	95.5%	(.f32 (/.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))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
	30.8%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (exp.f32 (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32)) #s(literal 3 binary32))) (/.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) (.f32 cosTheta (fma.f32 cosTheta cosTheta #s(literal 0 binary32))))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (.f32 cosTheta (exp.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)))))) (.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32)))) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)))))
	95.7%	(.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))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
	95.1%	(*.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))))
▶	93.2%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 619 to 878 computations (45.8% saved)

simplify246.0ms (1.9%)

Memory

-1.1MiB live, 370.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
✓	cost-diff	0	(fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	32	(-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))
✓	cost-diff	64	(neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) #s(literal -1 binary32))))
✓	cost-diff	96	(+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
✓	cost-diff	480	(-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	512	(*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) #s(literal -1 binary32)))
✓	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	-32	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
✓	cost-diff	0	(/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta)
✓	cost-diff	0	(fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) 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 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))

Rules

5 944×	`accelerator-lowering-fma.f32`
5 944×	`accelerator-lowering-fma.f64`
2 230×	`-lowering-.f32`
2 230×	`-lowering-.f64`
1 642×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	379
1	103	374
2	257	369
3	572	350
4	1805	350
5	4771	343
6	7455	343
0	8023	324

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
1
(+ (* (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))
(/ (exp (* (neg cosTheta) cosTheta)) cosTheta)
(exp (* (neg cosTheta) cosTheta))
(* (neg cosTheta) cosTheta)
(neg cosTheta)
cosTheta
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(/ (- (- 1 cosTheta) cosTheta) (PI))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
(PI)
(+ 1 c)
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 (neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))))
1
(neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1)))
(* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))
c
(+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1)
(/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c))
(+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI)))))
(- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))
(/ (sqrt (/ 1 (PI))) cosTheta)
(sqrt (/ 1 (PI)))
(/ 1 (PI))
(PI)
cosTheta
(neg c)
-1
(/ 1 (+ (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (- 0 (* cosTheta cosTheta)))) (+ 1 c)))
1
(+ (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (- 0 (* cosTheta cosTheta)))) (+ 1 c))
(/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(/ (- (- 1 cosTheta) cosTheta) (PI))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(PI)
(exp (- 0 (* cosTheta cosTheta)))
(- 0 (* cosTheta cosTheta))
0
(* cosTheta cosTheta)
(+ 1 c)
c

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

localize330.0ms (2.6%)

Memory

-19.4MiB live, 248.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.2%	(/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) #s(literal -1 binary32)))))
✓	accuracy	98.0%	(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	56.8%	(*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) #s(literal -1 binary32)))
✓	accuracy	99.8%	(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	98.4%	(/.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	98.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.3%	(fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))

Samples

218.0ms

256×

valid

Compiler

Compiled 379 to 44 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-mult: 155.0ms (78.4% of total)

ival-div: 15.0ms (7.6% of total)

ival-add: 7.0ms (3.5% of total)

ival-sqrt: 7.0ms (3.5% of total)

ival-sub: 5.0ms (2.5% of total)

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

ival-neg: 3.0ms (1.5% of total)

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

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.4%)

Memory

-16.9MiB live, 57.8MiB allocated

Counts

23 → 312

Calls

Call 1

Inputs
#<alt (/ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))>
#<alt (+ (* (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))>
#<alt (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)>
#<alt (exp (* (neg cosTheta) cosTheta))>
#<alt (sqrt (PI))>
#<alt (PI)>
#<alt (* cosTheta (sqrt (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 (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))>
#<alt (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))>
#<alt (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1)))>
#<alt (- 0 (* cosTheta cosTheta))>
#<alt (/ 1 (+ (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (- 0 (* cosTheta cosTheta)))) (+ 1 c)))>
#<alt (+ (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (- 0 (* cosTheta cosTheta)))) (+ 1 c))>
#<alt (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)>
#<alt (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (/ (sqrt (/ 1 (PI))) cosTheta)>
#<alt (/ 1 (neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))))>

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

Calls

78 calls:

Time	Variable		Point	Expression
17.0ms	c	@	-inf	(neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1)))
9.0ms	cosTheta	@	-inf	(* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))
1.0ms	c	@	0	(* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))
1.0ms	cosTheta	@	inf	(* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))
1.0ms	cosTheta	@	inf	(/ 1 (neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))))

rewrite348.0ms (2.7%)

Memory

5.9MiB live, 706.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 140×	`/-lowering-/.f32`
4 140×	`/-lowering-/.f64`
2 758×	`-lowering-.f32`
2 758×	`-lowering-.f64`
2 332×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	262
1	303	237
2	2849	232
0	8395	230

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 802

Calls

Call 1

Inputs
(/ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
(+ (* (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))
(/ (exp (* (neg cosTheta) cosTheta)) cosTheta)
(exp (* (neg cosTheta) cosTheta))
(sqrt (PI))
(PI)
(* cosTheta (sqrt (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)))
(* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))
(- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))
(+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI)))))
(neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1)))
(- 0 (* cosTheta cosTheta))
(/ 1 (+ (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (- 0 (* cosTheta cosTheta)))) (+ 1 c)))
(+ (* (/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta) (exp (- 0 (* cosTheta cosTheta)))) (+ 1 c))
(/ (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) cosTheta)
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(- (- 1 cosTheta) cosTheta)
(/ (sqrt (/ 1 (PI))) cosTheta)
(/ 1 (neg (* c (+ (/ (+ 1 (- (/ (sqrt (/ 1 (PI))) cosTheta) (sqrt (/ 1 (PI))))) (neg c)) -1))))

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

simplify476.0ms (3.7%)

Memory

4.1MiB live, 880.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 426×	`accelerator-lowering-fma.f32`
7 426×	`accelerator-lowering-fma.f64`
6 930×	`-lowering-.f32`
6 930×	`-lowering-.f64`
3 482×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	912	9702
1	3076	8984
0	8283	8664

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

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

eval247.0ms (1.9%)

Memory: 39.1MiB live, 419.6MiB allocated
Compiler: Compiled 51 900 to 6 241 computations (88% saved)

prune309.0ms (2.4%)

Memory

-42.8MiB live, 554.3MiB allocated

Pruning

35 alts after pruning (32 fresh and 3 done)

	Pruned	Kept	Total
New	1 635	15	1 650
Fresh	7	17	24
Picked	3	2	5
Done	0	1	1
Total	1 645	35	1 680

Accuracy

100.0%

Counts

1 680 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(pow.f32 (pow.f32 (fma.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.2%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) cosTheta))
	53.0%	(/.f32 (/.f32 #s(literal -1 binary32) c) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32))))) c)))
▶	94.1%	(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))))
▶	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)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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)))
	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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
✓	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	94.8%	(/.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)))
	96.1%	(/.f32 #s(literal 1 binary32) (/.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)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
▶	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))))) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) cosTheta)))
	94.5%	(/.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)))
	92.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))))
	94.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
	52.9%	(/.f32 #s(literal 1 binary32) (.f32 c (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c))) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c))))
	94.4%	(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (/.f32 #s(literal -1 binary32) c) (neg.f32 c))))
	41.0%	(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (/.f32 (-.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))))
	51.0%	(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (neg.f32 c)) #s(literal -1 binary32)))))
	53.2%	(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))))
	40.9%	(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (neg.f32 c)) #s(literal -1 binary32)))))
	53.1%	(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)))))
✓	5.2%	(/.f32 #s(literal 1 binary32) c)
	53.1%	(/.f32 #s(literal -1 binary32) (.f32 c (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) c))))
	30.8%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (exp.f32 (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32)) #s(literal 3 binary32))) (/.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)))) (.f32 cosTheta (fma.f32 cosTheta cosTheta #s(literal 0 binary32))))))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (.f32 cosTheta (exp.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)))))) (.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32)))) (*.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta)))))
	52.8%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) c))) (/.f32 #s(literal -1 binary32) c))
	95.1%	(*.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))))
	95.0%	(.f32 cosTheta (fma.f32 (.f32 cosTheta (PI.f32)) (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
▶	93.3%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	93.2%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 614 to 990 computations (38.7% saved)

simplify269.0ms (2.1%)

Memory

24.9MiB live, 532.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32))))
✓	cost-diff	160	(*.f32 (PI.f32) (log.f32 (E.f32)))
✓	cost-diff	3200	(log.f32 (E.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 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))))
✓	cost-diff	96	(+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
✓	cost-diff	512	(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	cost-diff	0	(+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))))
✓	cost-diff	32	(-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))
✓	cost-diff	32	(.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))

Rules

7 894×	`accelerator-lowering-fma.f32`
7 894×	`accelerator-lowering-fma.f64`
3 314×	`-lowering-.f32`
3 314×	`-lowering-.f64`
1 674×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	352
1	116	350
2	257	346
3	623	332
4	1279	326
5	3435	326
6	7461	326
0	8103	304

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ c (+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)))))
1
(+ c (+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta))))
c
(+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)))
(* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta))
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(/ (- (- 1 cosTheta) cosTheta) (PI))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(PI)
(/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)
(exp (- 0 (* cosTheta cosTheta)))
(- 0 (* cosTheta cosTheta))
0
(* cosTheta cosTheta)
(/ 1 (/ 1 (* cosTheta (sqrt (PI)))))
1
(/ 1 (* cosTheta (sqrt (PI))))
(* cosTheta (sqrt (PI)))
cosTheta
(sqrt (PI))
(PI)
(/ cosTheta (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1)))))
cosTheta
(* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1))))
(+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1)))
1
(* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1))
(sqrt (/ 1 (PI)))
(/ 1 (PI))
(PI)
(+ (/ 1 cosTheta) -1)
(/ 1 cosTheta)
-1
(/ 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 (sqrt (* (PI) (log (E)))))
cosTheta
(sqrt (* (PI) (log (E))))
(* (PI) (log (E)))
(PI)
(log (E))
(E)

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

localize191.0ms (1.5%)

Memory

-18.2MiB live, 310.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	100.0%	(E.f32)
✓	accuracy	98.8%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	accuracy	96.9%	(log.f32 (E.f32))
✓	accuracy	99.8%	(-.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	98.3%	(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	97.5%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
✓	accuracy	98.6%	(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
✓	accuracy	98.4%	(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))))
✓	accuracy	98.0%	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	accuracy	98.8%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))))
✓	accuracy	98.2%	(.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))

Samples

115.0ms

256×

valid

Compiler

Compiled 364 to 47 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-div: 15.0ms (26.6% of total)

ival-mult: 14.0ms (24.8% of total)

ival-add: 9.0ms (16% of total)

ival-sqrt: 6.0ms (10.6% of total)

ival-sub: 3.0ms (5.3% of total)

ival-log: 3.0ms (5.3% of total)

ival-exp: 2.0ms (3.5% of total)

ival-e: 2.0ms (3.5% of total)

ival-pi: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series76.0ms (0.6%)

Memory

18.5MiB live, 131.5MiB allocated

Counts

25 → 264

Calls

Call 1

Inputs
#<alt (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta))>
#<alt (- 0 (* cosTheta cosTheta))>
#<alt (/ 1 (+ c (+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)))))>
#<alt (+ c (+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta))))>
#<alt (/ 1 (/ 1 (* cosTheta (sqrt (PI)))))>
#<alt (/ 1 (* cosTheta (sqrt (PI))))>
#<alt (sqrt (PI))>
#<alt (PI)>
#<alt (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1))))>
#<alt (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1)))>
#<alt (/ cosTheta (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1)))))>
#<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 (log (E))>
#<alt (* (PI) (log (E)))>
#<alt (sqrt (* (PI) (log (E))))>
#<alt (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (E)>

Outputs
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
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#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (* -1 (sqrt (/ 1 (PI))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (* -1 (sqrt (/ 1 (PI))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>

Calls

66 calls:

Time	Variable		Point	Expression
46.0ms	cosTheta	@	0	(* cosTheta (sqrt (* (PI) (log (E)))))
6.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
4.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
1.0ms	c	@	0	(/ 1 (+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c)))
1.0ms	cosTheta	@	inf	(+ (* (/ (+ (* (* cosTheta cosTheta) (+ (* (* cosTheta cosTheta) 1/2) -1)) 1) cosTheta) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (+ 1 c))

rewrite647.0ms (5.1%)

Memory

17.1MiB live, 874.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 452×	`-lowering-.f32`
6 452×	`-lowering-.f64`
4 554×	`accelerator-lowering-fma.f32`
4 554×	`accelerator-lowering-fma.f64`
3 836×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	243
1	326	224
2	2881	224
0	10240	213

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 1 269

Calls

Call 1

Inputs
(* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta))
(- 0 (* cosTheta cosTheta))
(/ 1 (+ c (+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta)))))
(+ c (+ 1 (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (- 0 (* cosTheta cosTheta))) cosTheta))))
(/ 1 (/ 1 (* cosTheta (sqrt (PI)))))
(/ 1 (* cosTheta (sqrt (PI))))
(sqrt (PI))
(PI)
(* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1))))
(+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1)))
(/ cosTheta (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1)))))
(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)
(log (E))
(* (PI) (log (E)))
(sqrt (* (PI) (log (E))))
(sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))
(- (- 1 cosTheta) cosTheta)
(* cosTheta (sqrt (PI)))
(* (sqrt (/ 1 (PI))) (+ (/ 1 cosTheta) -1))
(* cosTheta (sqrt (* (PI) (log (E)))))
(E)

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

simplify536.0ms (4.2%)

Memory

-3.9MiB live, 912.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 486×	`accelerator-lowering-fma.f32`
10 486×	`accelerator-lowering-fma.f64`
8 268×	`-lowering-.f32`
8 268×	`-lowering-.f64`
5 090×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	804	8374
1	2589	7961
0	8554	7569

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) cosTheta)))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(/.f32 (fma.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta cosTheta))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))
(.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.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)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))
(fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal 1/2 binary32)) (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.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)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (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 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal 1/2 binary32)) (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.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)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (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 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) #s(literal 1/16 binary32)) (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal 1/2 binary32)) (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(neg.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32)))) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (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 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)) (.f32 (/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal -1/2 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (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 cosTheta (.f32 cosTheta (PI.f32)))))) (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32)))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (fma.f32 (.f32 #s(literal -1/16 binary32) (/.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (.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))))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))))))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(* -1 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta 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 (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(-.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta 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 (neg.f32 (.f32 cosTheta 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 (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(fma.f32 c (+.f32 (/.f32 c (pow.f32 (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta 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 (neg.f32 (.f32 cosTheta 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 (neg.f32 (*.f32 cosTheta 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 (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (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 (neg.f32 (.f32 cosTheta 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 (neg.f32 (.f32 cosTheta 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 (neg.f32 (.f32 cosTheta 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 (neg.f32 (.f32 cosTheta 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 (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta 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 (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/.f32 (+.f32 (/.f32 (pow.f32 (fma.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta 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)) (-.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
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(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) c) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 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))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32)) c) (.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))) (neg.f32 c)) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)) (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 (fma.f32 cosTheta (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.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 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
(* 1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (sqrt -2)))
(.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 1/2 binary32)))
(* (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))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (neg.f32 (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 1/2 binary32)) (.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32)))))))
(* (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))))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 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 5 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32))))))))))
(* (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)))))))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (fma.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 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 5 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 #s(literal 1/32 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 1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (fma.f32 #s(literal 1/4 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.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 (PI.f32) (pow.f32 cosTheta #s(literal 11 binary32))))) (sqrt.f32 #s(literal -2 binary32))) (fma.f32 (sqrt.f32 #s(literal -2 binary32)) (fma.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32)))))))))))))
(* -1/2 (* (sqrt (/ (pow cosTheta 7) (PI))) (* (sqrt -1) (sqrt 2))))
(.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 7 binary32)) (PI.f32))) (.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal -1/2 binary32)))
(* (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))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (fma.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/4 binary32)))) (neg.f32 (*.f32 cosTheta cosTheta)))))
(* (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)))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 (-.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) #s(literal -1/16 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)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/4 binary32)))) (*.f32 cosTheta cosTheta))))
(* (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))))))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 (-.f32 (-.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 c (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) #s(literal 1/8 binary32)) (.f32 #s(literal 1/32 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))))) (pow.f32 cosTheta #s(literal 6 binary32)))) (/.f32 (fma.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (fma.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) #s(literal -1/16 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)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) #s(literal 1/4 binary32)))) (.f32 cosTheta cosTheta))))
(+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (+.f32 c #s(literal 1 binary32)))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (+.f32 c #s(literal 1 binary32)))
(+ 1 (+ c (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (+.f32 c #s(literal 1 binary32)))
c
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) c)
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) c)
(* c (+ 1 (+ (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(fma.f32 c (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta c)) (/.f32 #s(literal 1 binary32) c)) c)
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (+.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (+.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (+.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta)
(/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)
(/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)
(/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)
(* 1/2 (pow cosTheta 3))
(.f32 #s(literal 1/2 binary32) (.f32 cosTheta (*.f32 cosTheta cosTheta)))
(* (pow cosTheta 3) (- 1/2 (/ 1 (pow cosTheta 2))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* (pow cosTheta 3) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(* (pow cosTheta 3) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(* 1/2 (pow cosTheta 3))
(.f32 #s(literal 1/2 binary32) (.f32 cosTheta (*.f32 cosTheta cosTheta)))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) 1/2)))
(.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))
(.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))))
(* -1 (* (pow cosTheta 3) (- (/ 1 (pow cosTheta 2)) (+ 1/2 (/ 1 (pow cosTheta 4))))))
(.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 cosTheta (.f32 cosTheta cosTheta))))
1
#s(literal 1 binary32)
(+ 1 (* -1 (pow cosTheta 2)))
(fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))
(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))
(fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))
(* 1/2 (pow cosTheta 4))
(*.f32 #s(literal 1/2 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))
(* (pow cosTheta 4) (- 1/2 (/ 1 (pow cosTheta 2))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* (pow cosTheta 4) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(* (pow cosTheta 4) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(* 1/2 (pow cosTheta 4))
(*.f32 #s(literal 1/2 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))
(* (pow cosTheta 4) (- 1/2 (/ 1 (pow cosTheta 2))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* (pow cosTheta 4) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(* (pow cosTheta 4) (- (+ 1/2 (/ 1 (pow cosTheta 4))) (/ 1 (pow cosTheta 2))))
(.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(fma.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1/2 binary32) cosTheta #s(literal -1/2 binary32)))))
(* (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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))) (sqrt.f32 #s(literal -2 binary32))))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (sqrt.f32 #s(literal 2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(neg.f32 (.f32 cosTheta (fma.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal 1/2 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)))))))
(neg.f32 (.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 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal 1/2 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))))))))
(neg.f32 (.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 (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)) (fma.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (PI.f32)))))) #s(literal 1/2 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
#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))
(*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))
(* cosTheta (- (/ 1 cosTheta) 2))
(*.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32)))
(* -2 cosTheta)
(*.f32 cosTheta #s(literal -2 binary32))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(-.f32 #s(literal 0 binary32) (*.f32 cosTheta (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(-.f32 #s(literal 0 binary32) (*.f32 cosTheta (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(-.f32 #s(literal 0 binary32) (*.f32 cosTheta (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1 binary32) cosTheta))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* (/ 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 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) 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 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (sqrt (* (PI) (log (E)))))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))

eval263.0ms (2.1%)

Memory: 22.7MiB live, 495.1MiB allocated
Compiler: Compiled 63 272 to 6 829 computations (89.2% saved)

prune314.0ms (2.5%)

Memory

-24.8MiB live, 692.7MiB allocated

Pruning

52 alts after pruning (46 fresh and 6 done)

	Pruned	Kept	Total
New	1 789	27	1 816
Fresh	8	19	27
Picked	2	3	5
Done	0	3	3
Total	1 799	52	1 851

Accuracy

100.0%

Counts

1 851 → 52

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(pow.f32 (pow.f32 (fma.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 0 binary32))) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	55.4%	(pow.f32 (*.f32 (+.f32 c (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32))) (+.f32 c (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))) #s(literal -1/2 binary32))
	56.1%	(/.f32 (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))) cosTheta)
	95.2%	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) cosTheta))
	53.0%	(/.f32 (/.f32 #s(literal -1 binary32) c) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32))))) c)))
	94.4%	(/.f32 cosTheta (fma.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) cosTheta cosTheta))
	94.2%	(/.f32 cosTheta (fma.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) cosTheta))
	94.4%	(/.f32 cosTheta (+.f32 (*.f32 cosTheta (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta))
	94.3%	(/.f32 cosTheta (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
	94.1%	(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))) (PI.f32)))))
	94.3%	(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (neg.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))))
	50.7%	(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32))))))
	50.6%	(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))))
	92.2%	(/.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	97.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.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 (-.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (.f32 (PI.f32) 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)))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 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)))
	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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 #s(literal 1 binary32) c)))
✓	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	94.8%	(/.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)))
	96.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)))
	92.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	93.0%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
	93.0%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
✓	93.1%	(/.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 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32)))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) c))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) cosTheta)))
	94.5%	(/.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)))
	92.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta)))))
	94.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	94.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
	94.4%	(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (/.f32 #s(literal -1 binary32) c) (neg.f32 c))))
	41.0%	(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (/.f32 (-.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) #s(literal 1 binary32)) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))))
	51.0%	(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (neg.f32 c)) #s(literal -1 binary32)))))
	53.2%	(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))))
	53.1%	(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)))))
✓	5.2%	(/.f32 #s(literal 1 binary32) c)
	54.1%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta)) (neg.f32 (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))))) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))))
	95.0%	(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)
	30.8%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 c (.f32 c c) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (.f32 cosTheta (exp.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)))))) #s(literal 3 binary32)))) (fma.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (.f32 cosTheta (exp.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)))))) (-.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (.f32 cosTheta (exp.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)))))) c) (.f32 c c)))
	51.2%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))) (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	52.8%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) c))) (/.f32 #s(literal -1 binary32) c))
	95.1%	(*.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))))
	95.0%	(.f32 cosTheta (fma.f32 (.f32 cosTheta (PI.f32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
✓	93.3%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	93.2%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 3 443 to 1 190 computations (65.4% saved)

regimes196.0ms (1.5%)

Memory

12.3MiB live, 320.0MiB allocated

Counts

89 → 1

Calls

Call 1

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

Calls

6 calls:

45.0ms	c
41.0ms	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)))))
27.0ms	(.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 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
98.5%	1	`cosTheta`
98.5%	1	`c`
98.5%	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)))))`
98.5%	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))))`
98.5%	1	`(+.f32 #s(literal 1 binary32) c)`
98.5%	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)

regimes121.0ms (1%)

Memory

1.8MiB live, 254.3MiB allocated

Counts

70 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

regimes119.0ms (0.9%)

Memory

-10.6MiB live, 185.2MiB allocated

Counts

62 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

26.0ms	cosTheta
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)))))
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))))
17.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
16.0ms	c

Results

Accuracy	Segments	Branch
97.9%	1	`cosTheta`
97.9%	1	`c`
97.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.9%	1	`(+.f32 #s(literal 1 binary32) c)`
97.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes85.0ms (0.7%)

Memory

8.5MiB live, 161.1MiB allocated

Counts

48 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 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) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 cosTheta (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (+.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(.f32 cosTheta (fma.f32 (.f32 cosTheta (PI.f32)) (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(.f32 cosTheta (fma.f32 (.f32 cosTheta (PI.f32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
(/.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 cosTheta (fma.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) cosTheta cosTheta))
(*.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 (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) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 cosTheta (+.f32 (*.f32 cosTheta (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta))
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)
(/.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 cosTheta (fma.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) 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 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))))
(/.f32 (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))) cosTheta)
(/.f32 #s(literal -1 binary32) (.f32 c (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) 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 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (neg.f32 c)) #s(literal -1 binary32)))))
(/.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 (/.f32 #s(literal -1 binary32) c) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32))))) c)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (/.f32 #s(literal -1 binary32) c) (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)))))
(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))) (PI.f32)))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) c))) (/.f32 #s(literal -1 binary32) c))
(/.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 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #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 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) c))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.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)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))))
(/.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.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 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (neg.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))))
(/.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 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) #s(literal -1 binary32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32))))))

Outputs

(/.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)))

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`c`
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)))`
97.5%	1	`cosTheta`
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)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes82.0ms (0.6%)

Memory

2.9MiB live, 199.6MiB allocated

Counts

46 → 1

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) c)
(*.f32 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) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 cosTheta (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (+.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(.f32 cosTheta (fma.f32 (.f32 cosTheta (PI.f32)) (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
(.f32 cosTheta (fma.f32 (.f32 cosTheta (PI.f32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))
(/.f32 cosTheta (*.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(/.f32 cosTheta (fma.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) cosTheta cosTheta))
(*.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 (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) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 cosTheta (+.f32 (*.f32 cosTheta (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))) cosTheta))
(*.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)
(/.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 cosTheta (fma.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) 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 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))))
(/.f32 (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32))))) cosTheta)
(/.f32 #s(literal -1 binary32) (.f32 c (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) 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 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (neg.f32 c)) #s(literal -1 binary32)))))
(/.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 (/.f32 #s(literal -1 binary32) c) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (sqrt.f32 (PI.f32))))) c)))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32)))))) (/.f32 #s(literal -1 binary32) c) (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (neg.f32 (*.f32 c (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)))))
(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))) (PI.f32)))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (sqrt.f32 (PI.f32))))) c))) (/.f32 #s(literal -1 binary32) c))
(/.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 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #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 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) #s(literal 1 binary32)) c))
(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) c) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (*.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) (fma.f32 (fma.f32 cosTheta cosTheta #s(literal 0 binary32)) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta cosTheta #s(literal 0 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.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)) (+.f32 #s(literal 1 binary32) c)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (neg.f32 (.f32 c (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (-.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))))
(/.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.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 cosTheta (.f32 cosTheta (+.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (neg.f32 (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))))))

Outputs

(/.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)))

Calls

6 calls:

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

regimes99.0ms (0.8%)

Memory

-31.8MiB live, 113.1MiB allocated

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

38.0ms	(/.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)))))
20.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	c
9.0ms	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes59.0ms (0.5%)

Memory

23.8MiB live, 101.2MiB allocated

Counts

33 → 1

Calls

Call 1

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

12.0ms	c
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 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
96.8%	1	`cosTheta`
96.8%	1	`c`
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 #s(literal 1 binary32) c)`
96.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes49.0ms (0.4%)

Memory

20.5MiB live, 95.7MiB allocated

Counts

26 → 1

Calls

Call 1

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

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:

9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
8.0ms	(+.f32 #s(literal 1 binary32) c)
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
7.0ms	c

Results

Accuracy	Segments	Branch
95.1%	1	`cosTheta`
95.1%	1	`c`
95.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
95.1%	1	`(+.f32 #s(literal 1 binary32) c)`
95.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes30.0ms (0.2%)

Memory

-24.2MiB live, 55.9MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

6 calls:

7.0ms	c
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
5.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.0%	1	`cosTheta`
95.0%	1	`c`
95.0%	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)))))`
95.0%	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))))`
95.0%	1	`(+.f32 #s(literal 1 binary32) c)`
95.0%	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)

regimes22.0ms (0.2%)

Memory

4.5MiB live, 43.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

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

regimes17.0ms (0.1%)

Memory

-3.6MiB live, 35.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
94.3%	1	`cosTheta`
94.3%	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)))))`
94.3%	1	`(+.f32 #s(literal 1 binary32) c)`
94.3%	1	`c`
94.3%	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))))`
94.3%	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)

regimes16.0ms (0.1%)

Memory

-6.7MiB live, 32.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

6 calls:

3.0ms	cosTheta
3.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
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	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	c

Results

Accuracy	Segments	Branch
93.2%	1	`c`
93.2%	1	`cosTheta`
93.2%	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)))))`
93.2%	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))))`
93.2%	1	`(+.f32 #s(literal 1 binary32) c)`
93.2%	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)

regimes9.0ms (0.1%)

Memory

31.0MiB live, 31.0MiB 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:

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

Results

Accuracy	Segments	Branch
5.2%	1	`c`
5.2%	1	`(+.f32 #s(literal 1 binary32) c)`
5.2%	1	`cosTheta`
5.2%	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)))))`
5.2%	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))))`
5.2%	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)

simplify14.0ms (0.1%)

Memory

-14.3MiB live, 27.3MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary32`
30×	`+-commutative_binary32`
18×	`sub-neg_binary32`
10×	`neg-sub0_binary32`
10×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	240
1	111	240
2	128	240
3	137	240
4	141	240

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

soundness1.2s (9.6%)

Memory

5.2MiB live, 1 102.0MiB allocated

Rules

10 486×	`accelerator-lowering-fma.f32`
10 486×	`accelerator-lowering-fma.f64`
9 656×	`accelerator-lowering-fma.f32`
9 656×	`accelerator-lowering-fma.f64`
8 268×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	852	12606
1	2924	12025
0	8112	11532
0	40	275
1	285	257
2	2345	257
0	9560	254
0	45	243
1	326	224
2	2881	224
0	10240	213
0	410	3676
1	1246	3572
2	4769	3476
0	8360	3311
0	912	9702
1	3076	8984
0	8283	8664
0	804	8374
1	2589	7961
0	8554	7569
0	18	89
1	126	80
2	1045	73
0	8540	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

Compiler

Compiled 658 to 340 computations (48.3% saved)

preprocess329.0ms (2.6%)

Memory: -164.4MiB live, 212.3MiB allocated
Compiler: Compiled 542 to 192 computations (64.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze27.0ms (0.2%)

sample2.0s (15.5%)

preprocess360.0ms (2.8%)

explain312.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify174.0ms (1.4%)

localize53.0ms (0.4%)

series24.0ms (0.2%)

rewrite318.0ms (2.5%)

simplify456.0ms (3.6%)

eval68.0ms (0.5%)

prune98.0ms (0.8%)

simplify264.0ms (2.1%)

localize146.0ms (1.2%)

series43.0ms (0.3%)

rewrite530.0ms (4.2%)

simplify637.0ms (5%)

eval209.0ms (1.6%)

prune242.0ms (1.9%)

simplify246.0ms (1.9%)

localize330.0ms (2.6%)

series50.0ms (0.4%)

rewrite348.0ms (2.7%)

simplify476.0ms (3.7%)

eval247.0ms (1.9%)

prune309.0ms (2.4%)

simplify269.0ms (2.1%)

localize191.0ms (1.5%)

series76.0ms (0.6%)

rewrite647.0ms (5.1%)

simplify536.0ms (4.2%)

eval263.0ms (2.1%)

prune314.0ms (2.5%)

regimes196.0ms (1.5%)

regimes121.0ms (1%)

regimes119.0ms (0.9%)

regimes85.0ms (0.7%)

regimes82.0ms (0.6%)

regimes99.0ms (0.8%)

regimes59.0ms (0.5%)

regimes49.0ms (0.4%)

regimes30.0ms (0.2%)

regimes22.0ms (0.2%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

regimes9.0ms (0.1%)

simplify14.0ms (0.1%)

soundness1.2s (9.6%)

preprocess329.0ms (2.6%)

end0.0ms (0%)

Profiling