Metrics for Beckmann Sample, normalization factor

analyze28.0ms (0.2%)

Memory

1.3MiB live, 41.7MiB 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 (15.6%)

Memory

58.4MiB live, 3 591.0MiB allocated

Samples

1.5s	8 256×	0	valid
7.0ms	44×	0	invalid

Precisions

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

ival-div: 356.0ms (27.4% of total)

ival-mult: 165.0ms (12.7% of total)

ival-exp: 137.0ms (10.5% of total)

const: 130.0ms (10% of total)

ival-sqrt: 119.0ms (9.1% of total)

ival-add: 115.0ms (8.8% of total)

ival-sub: 90.0ms (6.9% of total)

ival-<: 81.0ms (6.2% of total)

ival-neg: 37.0ms (2.8% of total)

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

ival-and: 22.0ms (1.7% of total)

exact: 15.0ms (1.2% of total)

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

Bogosity

preprocess260.0ms (2%)

Memory

-19.4MiB live, 179.3MiB allocated

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

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

Outputs

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

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

Call 2

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

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

explain505.0ms (4%)

Memory

-10.6MiB live, 387.2MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f32`	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

95.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

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

ival-div: 10.0ms (23.2% of total)

ival-mult: 8.0ms (18.6% of total)

ival-sqrt: 7.0ms (16.3% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

97.6%

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

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify221.0ms (1.7%)

Memory

16.0MiB live, 123.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize113.0ms (0.9%)

Memory

22.4MiB live, 106.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	97.8%	(*.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

92.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-pi: 33.0ms (56.2% of total)

ival-sqrt: 9.0ms (15.3% of total)

ival-div: 5.0ms (8.5% of total)

ival-mult: 4.0ms (6.8% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.2%)

Memory

4.1MiB live, 42.8MiB allocated

Counts

6 → 84

Calls

Call 1

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

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

Calls

21 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta	@	-inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
4.0ms	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))
1.0ms	cosTheta	@	-inf	(* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))

rewrite579.0ms (4.6%)

Memory

-21.3MiB live, 578.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 473

Calls

Call 1

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

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

simplify394.0ms (3.1%)

Memory

-19.8MiB live, 632.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

eval67.0ms (0.5%)

Memory: 10.0MiB live, 165.1MiB allocated
Compiler: Compiled 23 196 to 2 836 computations (87.8% saved)

prune101.0ms (0.8%)

Memory

18.4MiB live, 349.3MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	530	27	557
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	531	27	558

Accuracy

99.9%

Counts

558 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.4%	(pow.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	31.4%	(/.f32 (fma.f32 (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal -1 binary32) (neg.f32 c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))) (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))))
	55.5%	(/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (neg.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (*.f32 cosTheta (neg.f32 cosTheta))))))))
▶	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)))
	52.6%	(/.f32 #s(literal 1 binary32) (fma.f32 c (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (.f32 cosTheta c)) #s(literal 1 binary32)) #s(literal 1 binary32)))
	98.1%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (+.f32 c #s(literal -1 binary32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
▶	95.4%	(/.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 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
	96.7%	(/.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)))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
	95.4%	(/.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)))
	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))))
▶	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	52.7%	(/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal -1 binary32) (/.f32 (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32)) c)) (neg.f32 c)))
▶	4.7%	(/.f32 #s(literal 1 binary32) c)
	55.5%	(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (neg.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (.f32 cosTheta (neg.f32 cosTheta)))))))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta)))
	96.1%	(*.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))))
	94.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.1%	(exp.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c)) #s(literal -1 binary32)))

Compiler

Compiled 1 536 to 860 computations (44% saved)

simplify295.0ms (2.3%)

Memory

-28.2MiB live, 726.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f32 c c #s(literal -1 binary32))
✓	cost-diff	160	(fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))))))
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
✓	cost-diff	512	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta))
✓	cost-diff	0	(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
✓	cost-diff	0	(/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta)
✓	cost-diff	0	(fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	0	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	0	(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
✓	cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
✓	cost-diff	576	(fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.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	64	(.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

11 726×	`accelerator-lowering-fma.f32`
11 726×	`accelerator-lowering-fma.f64`
3 006×	`-lowering-.f32`
3 006×	`-lowering-.f64`
1 846×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	452
1	111	452
2	246	442
3	614	429
4	1515	413
5	4225	413
0	8287	384

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

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

localize156.0ms (1.2%)

Memory

24.6MiB live, 418.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
✓	accuracy	98.5%	(/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.0%	(fma.f32 (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (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	98.4%	(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
✓	accuracy	96.9%	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	99.1%	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	accuracy	98.9%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

86.0ms

256×

valid

Compiler

Compiled 437 to 51 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-div: 21.0ms (31.3% of total)

ival-mult: 16.0ms (23.9% of total)

ival-sqrt: 10.0ms (14.9% of total)

ival-add: 9.0ms (13.4% of total)

ival-exp: 4.0ms (6% of total)

ival-sub: 4.0ms (6% of total)

ival-pi: 1.0ms (1.5% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series73.0ms (0.6%)

Memory

6.2MiB live, 170.4MiB allocated

Counts

25 → 420

Calls

Call 1

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

Calls

105 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta	@	-inf	(/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (exp (* cosTheta (neg cosTheta)))))) (* (+ c -1) cosTheta)))
6.0ms	c	@	inf	(+ (* c c) -1)
4.0ms	cosTheta	@	inf	(/ 1 (/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (exp (* cosTheta (neg cosTheta)))))) (* (+ c -1) cosTheta)))
3.0ms	cosTheta	@	inf	(/ 1 (/ (+ (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) cosTheta))
3.0ms	c	@	inf	(/ (+ (* (+ (* c c) -1) cosTheta) (* (+ c -1) (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (exp (* cosTheta (neg cosTheta)))))) (* (+ c -1) cosTheta))

rewrite493.0ms (3.9%)

Memory

-6.0MiB live, 425.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 328×	`/-lowering-/.f32`
4 328×	`/-lowering-/.f64`
3 222×	`-lowering-.f32`
3 222×	`-lowering-.f64`
2 404×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	338
1	323	326
2	2846	326
0	8726	308

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 906

Calls

Call 1

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

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

simplify620.0ms (4.9%)

Memory

-10.4MiB live, 396.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6 886×	`-lowering-.f32`
6 886×	`-lowering-.f64`
6 434×	`accelerator-lowering-fma.f32`
6 434×	`accelerator-lowering-fma.f64`
4 514×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1183	16075
1	3925	15574
0	8568	14879

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

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

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

eval264.0ms (2.1%)

Memory: 11.6MiB live, 204.4MiB allocated
Compiler: Compiled 59 641 to 5 675 computations (90.5% saved)

prune299.0ms (2.4%)

Memory

15.7MiB live, 257.2MiB allocated

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	1 520	19	1 539
Fresh	15	7	22
Picked	4	1	5
Done	0	0	0
Total	1 539	27	1 566

Accuracy

100.0%

Counts

1 566 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.2%	(pow.f32 (pow.f32 (/.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) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	31.4%	(/.f32 (fma.f32 (/.f32 (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) cosTheta) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (+.f32 #s(literal -1 binary32) (neg.f32 c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))) (exp.f32 (.f32 (.f32 cosTheta (neg.f32 cosTheta)) #s(literal 3 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))))
	95.6%	(/.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))
▶	97.9%	(/.f32 (neg.f32 cosTheta) (neg.f32 (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	95.4%	(/.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)))))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.6%	(/.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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
▶	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (*.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	95.6%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1 binary32)))) (*.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	95.7%	(/.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 cosTheta (+.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))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	95.4%	(/.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)))))))
	95.4%	(/.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)))
	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	98.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))))
	49.9%	(/.f32 #s(literal 1 binary32) (.f32 c (-.f32 (+.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)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))
✓	4.7%	(/.f32 #s(literal 1 binary32) c)
	96.3%	(.f32 (/.f32 cosTheta (fma.f32 (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (sqrt.f32 (PI.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 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 cosTheta (*.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))) (sqrt.f32 (PI.f32)))))
	96.4%	(.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 cosTheta (+.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)))))
	96.1%	(*.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))))
	98.6%	(.f32 cosTheta (/.f32 (+.f32 c #s(literal -1 binary32)) (fma.f32 cosTheta (fma.f32 c c #s(literal -1 binary32)) (.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 (+.f32 c #s(literal -1 binary32)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))))))
▶	94.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 489 to 782 computations (47.5% saved)

simplify207.0ms (1.6%)

Memory

15.3MiB live, 362.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
✓	cost-diff	0	(neg.f32 (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))
✓	cost-diff	0	(neg.f32 cosTheta)
✓	cost-diff	128	(/.f32 (neg.f32 cosTheta) (neg.f32 (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
✓	cost-diff	0	(/.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)))))
✓	cost-diff	64	(/.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)))))))
✓	cost-diff	576	(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))))
✓	cost-diff	640	(/.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))))))
✓	cost-diff	0	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	96	(fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))))

Rules

6 578×	`accelerator-lowering-fma.f32`
6 578×	`accelerator-lowering-fma.f64`
2 274×	`-lowering-.f32`
2 274×	`-lowering-.f64`
1 450×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	367
1	94	363
2	224	356
3	633	354
4	1590	350
5	5170	350
0	8098	325

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize139.0ms (1.1%)

Memory

-2.1MiB live, 240.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.7%	(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
✓	accuracy	98.3%	(/.f32 (neg.f32 cosTheta) (neg.f32 (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	98.3%	(/.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)))))
✓	accuracy	97.1%	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.0%	(fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.7%	(/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
✓	accuracy	99.2%	(/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))))
✓	accuracy	99.0%	(*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))

Samples

78.0ms

256×

valid

Compiler

Compiled 353 to 43 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-div: 19.0ms (33.2% of total)

ival-mult: 16.0ms (27.9% of total)

ival-add: 9.0ms (15.7% of total)

ival-sqrt: 5.0ms (8.7% of total)

ival-exp: 3.0ms (5.2% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series44.0ms (0.3%)

Memory

3.1MiB live, 80.5MiB allocated

Counts

25 → 348

Calls

Call 1

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

Outputs
#<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))))))>
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#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -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 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (/ 1 (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))))>
#<alt (/ 1 (- 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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 2))))) (/ 1 (- 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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 3)))))) (pow cosTheta 4))) (/ 1 (- 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 (* (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 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 3)))))))) (* (sqrt 2) (- 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))) (pow cosTheta 6))) (/ 1 (- 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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 3)))))))))>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 (sqrt (/ 1 (PI))))>
#<alt (- (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))>
#<alt (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))>
#<alt (- (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))>
#<alt (* -1 (* cosTheta (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (* cosTheta (- (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (* cosTheta (- (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ 1 (+ (* 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 (* cosTheta (- (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ 1 (+ (* -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 (* cosTheta (- 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))>
#<alt (* -1 (* cosTheta (- (+ 1 (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))>
#<alt (* -1 (* cosTheta (- (+ 1 (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))>
#<alt (* -1 (* cosTheta (- (+ 1 (* -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)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))>
#<alt (sqrt (/ 1 (PI)))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))>
#<alt (* cosTheta (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (* cosTheta (+ 1 (+ (* 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 (* cosTheta (+ 1 (+ (* -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 (* cosTheta (+ 1 (+ (* -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 (* cosTheta (- (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))) 1)))>
#<alt (* -1 (* cosTheta (- (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 1)))>
#<alt (* -1 (* cosTheta (- (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 1)))>
#<alt (* -1 (* cosTheta (- (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 1)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (sqrt (PI)))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* -1/2 (* (* cosTheta (+ (PI) (* -4 (PI)))) (sqrt (/ 1 (PI)))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI))))) (* -1/2 (* (* cosTheta (+ (* -8 (PI)) (* -1 (+ (PI) (* -4 (PI)))))) (sqrt (/ 1 (PI)))))))))))>
#<alt (* (sqrt (* cosTheta (PI))) (sqrt -1/2))>
#<alt (* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))>
#<alt (* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2)))))>
#<alt (* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (+ (* 1/64 (/ (* cosTheta (PI)) (pow (sqrt -1/2) 2))) (* 1/16 (PI))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))))>
#<alt (* (sqrt (* cosTheta (PI))) (* (sqrt -1) (sqrt 1/2)))>
#<alt (* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))>
#<alt (* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))>
#<alt (* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (+ (* -1/64 (/ (* cosTheta (PI)) (pow (sqrt 1/2) 2))) (* 1/16 (PI)))) (sqrt 1/2)))) (* -1/16 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))>
#<alt (PI)>
#<alt (+ (PI) (* 2 (* cosTheta (PI))))>
#<alt (+ (PI) (* cosTheta (- (* 4 (* cosTheta (PI))) (* -2 (PI)))))>
#<alt (+ (PI) (* cosTheta (- (* cosTheta (- (* 8 (* cosTheta (PI))) (* -4 (PI)))) (* -2 (PI)))))>
#<alt (* -1/2 (/ (PI) cosTheta))>
#<alt (/ (+ (* -1/2 (PI)) (* -1/4 (/ (PI) cosTheta))) cosTheta)>
#<alt (/ (- (+ (* -1/2 (PI)) (* -1/8 (/ (PI) (pow cosTheta 2)))) (* 1/4 (/ (PI) cosTheta))) cosTheta)>
#<alt (/ (- (+ (* -1/2 (PI)) (* -1/16 (/ (PI) (pow cosTheta 3)))) (+ (* 1/8 (/ (PI) (pow cosTheta 2))) (* 1/4 (/ (PI) cosTheta)))) cosTheta)>
#<alt (* -1/2 (/ (PI) cosTheta))>
#<alt (* -1 (/ (+ (* 1/4 (/ (PI) cosTheta)) (* 1/2 (PI))) cosTheta))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (PI) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (PI) cosTheta)) (* -1/8 (PI))) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))>
#<alt (/ 1 (PI))>
#<alt (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))>
#<alt (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))>
#<alt (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))>
#<alt (* -2 (/ cosTheta (PI)))>
#<alt (* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))>
#<alt (* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))>
#<alt (* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))>
#<alt (* -2 (/ cosTheta (PI)))>
#<alt (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))>
#<alt (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))>
#<alt (* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))>
#<alt (+ 1 (* -1 (sqrt (/ 1 (PI)))))>
#<alt (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))>
#<alt (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))>
#<alt (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))>
#<alt c>
#<alt (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))>

Calls

87 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta	@	-inf	(/ (neg cosTheta) (neg (+ (* (exp (* cosTheta (neg cosTheta))) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) cosTheta)))
3.0ms	cosTheta	@	inf	(/ (neg cosTheta) (neg (+ (* (exp (* cosTheta (neg cosTheta))) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) cosTheta)))
2.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ 1 cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
2.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ 1 cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
2.0ms	cosTheta	@	0	(/ 1 (+ (+ 1 c) (/ (exp (* cosTheta (neg cosTheta))) (* cosTheta (sqrt (/ (PI) (- (- 1 cosTheta) cosTheta)))))))

rewrite313.0ms (2.5%)

Memory

7.8MiB live, 798.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 084×	`/-lowering-/.f32`
4 084×	`/-lowering-/.f64`
3 082×	`-lowering-.f32`
3 082×	`-lowering-.f64`
2 352×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	276
1	294	263
2	2824	263
0	8570	247

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 897

Calls

Call 1

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

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

simplify438.0ms (3.4%)

Memory

2.6MiB live, 1 076.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 222×	`-lowering-.f32`
7 222×	`-lowering-.f64`
6 732×	`accelerator-lowering-fma.f32`
6 732×	`accelerator-lowering-fma.f64`
5 082×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1147	11922
1	3751	11346
0	8530	10888

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(/ 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)))))))
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(/ 1 (- 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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 2))))) (/ 1 (- 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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 3)))))) (pow cosTheta 4))) (/ 1 (- 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 (* (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 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 3)))))))) (* (sqrt 2) (- 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))) (pow cosTheta 6))) (/ 1 (- 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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 3)))))))))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 (sqrt (/ 1 (PI))))
(- (* -1 (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))
(- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))
(- (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))
(* -1 (* cosTheta (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* cosTheta (- (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* cosTheta (- (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ 1 (+ (* 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)))))))
(* cosTheta (- (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ 1 (+ (* -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 (* cosTheta (- 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (- (+ 1 (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (- (+ 1 (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* cosTheta (- (+ 1 (* -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)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(* cosTheta (+ 1 (+ (* 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))))))
(* cosTheta (+ 1 (+ (* -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)))))))
(* cosTheta (+ 1 (+ (* -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 (* cosTheta (- (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))) 1)))
(* -1 (* cosTheta (- (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) 1)))
(* -1 (* cosTheta (- (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 1)))
(* -1 (* cosTheta (- (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 1)))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (sqrt (PI)))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* -1/2 (* (* cosTheta (+ (PI) (* -4 (PI)))) (sqrt (/ 1 (PI)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI))))) (* -1/2 (* (* cosTheta (+ (* -8 (PI)) (* -1 (+ (PI) (* -4 (PI)))))) (sqrt (/ 1 (PI)))))))))))
(* (sqrt (* cosTheta (PI))) (sqrt -1/2))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2)))))
(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (+ (* 1/64 (/ (* cosTheta (PI)) (pow (sqrt -1/2) 2))) (* 1/16 (PI))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))))
(* (sqrt (* cosTheta (PI))) (* (sqrt -1) (sqrt 1/2)))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (+ (* -1/64 (/ (* cosTheta (PI)) (pow (sqrt 1/2) 2))) (* 1/16 (PI)))) (sqrt 1/2)))) (* -1/16 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(PI)
(+ (PI) (* 2 (* cosTheta (PI))))
(+ (PI) (* cosTheta (- (* 4 (* cosTheta (PI))) (* -2 (PI)))))
(+ (PI) (* cosTheta (- (* cosTheta (- (* 8 (* cosTheta (PI))) (* -4 (PI)))) (* -2 (PI)))))
(* -1/2 (/ (PI) cosTheta))
(/ (+ (* -1/2 (PI)) (* -1/4 (/ (PI) cosTheta))) cosTheta)
(/ (- (+ (* -1/2 (PI)) (* -1/8 (/ (PI) (pow cosTheta 2)))) (* 1/4 (/ (PI) cosTheta))) cosTheta)
(/ (- (+ (* -1/2 (PI)) (* -1/16 (/ (PI) (pow cosTheta 3)))) (+ (* 1/8 (/ (PI) (pow cosTheta 2))) (* 1/4 (/ (PI) cosTheta)))) cosTheta)
(* -1/2 (/ (PI) cosTheta))
(* -1 (/ (+ (* 1/4 (/ (PI) cosTheta)) (* 1/2 (PI))) cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (PI) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (PI) cosTheta)) (* -1/8 (PI))) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))
(/ 1 (PI))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(* -2 (/ cosTheta (PI)))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* -2 (/ cosTheta (PI)))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
c
(* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))
(* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))
(* c (+ 1 (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) c)) 1)))

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

eval245.0ms (1.9%)

Memory: -8.5MiB live, 548.8MiB allocated
Compiler: Compiled 53 263 to 6 424 computations (87.9% saved)

prune269.0ms (2.1%)

Memory

-13.7MiB live, 626.9MiB allocated

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	1 708	18	1 726
Fresh	9	12	21
Picked	4	1	5
Done	0	1	1
Total	1 721	32	1 753

Accuracy

100.0%

Counts

1 753 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.6%	(/.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))
	97.9%	(/.f32 (neg.f32 cosTheta) (/.f32 (fma.f32 (exp.f32 (fma.f32 cosTheta (neg.f32 cosTheta) (.f32 cosTheta (neg.f32 cosTheta)))) (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 cosTheta (neg.f32 cosTheta))) (neg.f32 (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (neg.f32 cosTheta)))))
	97.9%	(/.f32 cosTheta (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))
	95.4%	(/.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)))))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.6%	(/.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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
▶	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))) (+.f32 #s(literal 1 binary32) c)))
	95.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	92.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 #s(literal 1 binary32) c)))
	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))) (+.f32 #s(literal 1 binary32) c)))
	97.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (fma.f32 c c #s(literal -1 binary32)) cosTheta (.f32 (+.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))))) (*.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
▶	95.5%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
	53.0%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (-.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	93.9%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))))
	50.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))))
✓	4.7%	(/.f32 #s(literal 1 binary32) c)
	53.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta)) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) (-.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
▶	96.1%	(*.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))))
	96.1%	(.f32 cosTheta (fma.f32 (neg.f32 (.f32 cosTheta (PI.f32))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))))
▶	98.6%	(.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	93.9%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	94.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 279 to 799 computations (37.5% saved)

simplify276.0ms (2.2%)

Memory

4.5MiB live, 395.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) cosTheta)
✓	cost-diff	256	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
✓	cost-diff	576	(fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
✓	cost-diff	800	(/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
✓	cost-diff	0	(fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))
✓	cost-diff	0	(fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	160	(/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))
✓	cost-diff	0	(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)))
✓	cost-diff	0	(*.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))))
✓	cost-diff	0	(sqrt.f32 (PI.f32))
✓	cost-diff	0	(*.f32 cosTheta (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	(exp.f32 (*.f32 cosTheta (neg.f32 cosTheta)))
✓	cost-diff	0	(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))
✓	cost-diff	160	(.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))

Rules

9 080×	`accelerator-lowering-fma.f32`
9 080×	`accelerator-lowering-fma.f64`
3 010×	`-lowering-.f32`
3 010×	`-lowering-.f64`
1 790×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	369
1	105	353
2	225	351
3	704	340
4	2235	340
5	5539	336
0	8268	313

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize153.0ms (1.2%)

Memory

19.7MiB live, 277.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	97.3%	(/.f32 #s(literal 1 binary32) (fma.f32 cosTheta (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))
✓	accuracy	96.9%	(+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.0%	(fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	99.6%	(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	99.0%	(*.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))))
✓	accuracy	97.1%	(fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.2%	(/.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	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.7%	(fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)
✓	accuracy	99.0%	(.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	97.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))

Samples

80.0ms

256×

valid

Compiler

Compiled 346 to 47 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-div: 21.0ms (33.9% of total)

ival-mult: 14.0ms (22.6% of total)

ival-add: 11.0ms (17.7% of total)

ival-sqrt: 8.0ms (12.9% of total)

ival-sub: 3.0ms (4.8% of total)

ival-exp: 2.0ms (3.2% of total)

ival-pi: 1.0ms (1.6% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series62.0ms (0.5%)

Memory

-21.2MiB live, 92.0MiB allocated

Counts

28 → 360

Calls

Call 1

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

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

Calls

90 calls:

Time	Variable		Point	Expression
13.0ms	c	@	0	(+ (* (/ (+ (* cosTheta (neg cosTheta)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c))
6.0ms	c	@	inf	(* cosTheta (+ (* (+ (* (PI) (- c (sqrt (/ 1 (PI))))) (PI)) (neg cosTheta)) (sqrt (PI))))
5.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (+ (* cosTheta (neg cosTheta)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
3.0ms	cosTheta	@	-inf	(* cosTheta (/ 1 (+ (* (exp (* cosTheta (neg cosTheta))) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) cosTheta)))
3.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* cosTheta (neg cosTheta)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))

rewrite799.0ms (6.3%)

Memory

-189.6MiB live, 715.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 152×	`-lowering-.f32`
6 152×	`-lowering-.f64`
6 144×	`accelerator-lowering-fma.f32`
6 144×	`accelerator-lowering-fma.f64`
3 592×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	294
1	321	263
2	2797	263
0	9852	244

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 1 214

Calls

Call 1

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

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

simplify429.0ms (3.4%)

Memory

29.2MiB live, 561.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 048×	`accelerator-lowering-fma.f32`
7 048×	`accelerator-lowering-fma.f64`
6 834×	`-lowering-.f32`
6 834×	`-lowering-.f64`
4 734×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	993	11062
1	3403	10418
0	8185	10005

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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

eval301.0ms (2.4%)

Memory: 59.9MiB live, 506.5MiB allocated
Compiler: Compiled 68 496 to 8 373 computations (87.8% saved)

prune412.0ms (3.2%)

Memory

-51.6MiB live, 785.7MiB allocated

Pruning

40 alts after pruning (36 fresh and 4 done)

	Pruned	Kept	Total
New	2 168	21	2 189
Fresh	10	15	25
Picked	3	2	5
Done	0	2	2
Total	2 181	40	2 221

Accuracy

100.0%

Counts

2 221 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.1%	(fma.f32 (fma.f32 (PI.f32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (.f32 cosTheta (neg.f32 cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32))))
	96.1%	(fma.f32 cosTheta (fma.f32 cosTheta (neg.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (neg.f32 c)))
	95.6%	(/.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))
	97.9%	(/.f32 cosTheta (fma.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta))
	95.4%	(/.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)))))
	54.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (neg.f32 cosTheta)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.6%	(/.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 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
✓	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	96.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	95.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))) (+.f32 #s(literal 1 binary32) c)))
	97.5%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (-.f32 (.f32 c c) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)) (.f32 (-.f32 c #s(literal 1 binary32)) (.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))))) (.f32 (-.f32 c #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))
	93.4%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
	93.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 c #s(literal -1 binary32))) (.f32 (+.f32 c #s(literal -1 binary32)) cosTheta)))
	93.4%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
✓	93.9%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))))))
	50.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (*.f32 cosTheta c)) #s(literal 1 binary32))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))))
✓	4.7%	(/.f32 #s(literal 1 binary32) c)
	53.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta)) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) (-.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	57.0%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))))
	93.4%	(.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (/.f32 (fma.f32 c (.f32 c c) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (sqrt.f32 (PI.f32))))) (+.f32 (fma.f32 c c (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 c (sqrt.f32 (PI.f32))))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	93.8%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) c (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	96.1%	(*.f32 cosTheta (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	96.1%	(*.f32 cosTheta (fma.f32 (+.f32 (PI.f32) (fma.f32 (PI.f32) c (neg.f32 (sqrt.f32 (PI.f32))))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	94.0%	(.f32 cosTheta (fma.f32 (.f32 (PI.f32) c) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	98.6%	(.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	98.5%	(.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	97.9%	(*.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	98.6%	(.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (E.f32) (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	96.3%	(*.f32 cosTheta (/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta)))
	95.4%	(.f32 cosTheta (.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)))))
	93.9%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	94.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	95.9%	(.f32 cosTheta (neg.f32 (.f32 c (fma.f32 cosTheta (PI.f32) (/.f32 (fma.f32 cosTheta (neg.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) (neg.f32 c))))))
	95.9%	(.f32 c (fma.f32 cosTheta (/.f32 (fma.f32 cosTheta (neg.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32))) c) (neg.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))

Compiler

Compiled 2 783 to 891 computations (68% saved)

regimes189.0ms (1.5%)

Memory

-3.3MiB live, 352.9MiB allocated

Counts

86 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

53.0ms	c
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)))
27.0ms	(+.f32 #s(literal 1 binary32) c)
25.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

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

regimes149.0ms (1.2%)

Memory

-8.6MiB live, 200.9MiB allocated

Counts

65 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

41.0ms	(+.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))))
32.0ms	(.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)))
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	cosTheta
18.0ms	c

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`c`
98.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.6%	1	`(+.f32 #s(literal 1 binary32) c)`
98.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes134.0ms (1.1%)

Memory

6.3MiB live, 199.4MiB allocated

Counts

61 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

39.0ms	cosTheta
20.0ms	(+.f32 #s(literal 1 binary32) c)
19.0ms	c
18.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
18.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.6%	1	`c`
98.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.6%	1	`(+.f32 #s(literal 1 binary32) c)`
98.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes114.0ms (0.9%)

Memory

-7.8MiB live, 231.0MiB allocated

Counts

60 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

24.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
18.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
17.0ms	c
17.0ms	cosTheta
17.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.6%	1	`c`
98.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.6%	1	`(+.f32 #s(literal 1 binary32) c)`
98.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes90.0ms (0.7%)

Memory

-9.9MiB live, 158.6MiB allocated

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
98.5%	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)

regimes61.0ms (0.5%)

Memory

26.3MiB live, 64.8MiB allocated

Counts

35 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

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)

regimes51.0ms (0.4%)

Memory

4.2MiB live, 80.1MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

6 calls:

17.0ms	(+.f32 #s(literal 1 binary32) c)
8.0ms	c
6.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
6.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
96.3%	1	`cosTheta`
96.3%	1	`c`
96.3%	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)))))`
96.3%	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))))`
96.3%	1	`(+.f32 #s(literal 1 binary32) c)`
96.3%	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)

regimes23.0ms (0.2%)

Memory

9.2MiB live, 50.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
(*.f32 cosTheta (fma.f32 (+.f32 (PI.f32) (fma.f32 (PI.f32) c (neg.f32 (sqrt.f32 (PI.f32))))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
96.1%	1	`c`
96.1%	1	`cosTheta`
96.1%	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)))))`
96.1%	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))))`
96.1%	1	`(+.f32 #s(literal 1 binary32) c)`
96.1%	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)

regimes24.0ms (0.2%)

Memory

-28.7MiB live, 48.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

Calls

6 calls:

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	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	(/.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	c

Results

Accuracy	Segments	Branch
96.1%	1	`cosTheta`
96.1%	1	`c`
96.1%	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)))))`
96.1%	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))))`
96.1%	1	`(+.f32 #s(literal 1 binary32) c)`
96.1%	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)

regimes13.0ms (0.1%)

Memory

33.4MiB live, 33.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
(.f32 cosTheta (fma.f32 (.f32 (PI.f32) c) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
94.0%	1	`cosTheta`
94.0%	1	`c`
94.0%	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)))))`
94.0%	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))))`
94.0%	1	`(+.f32 #s(literal 1 binary32) c)`
94.0%	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)

regimes12.0ms (0.1%)

Memory

-11.9MiB live, 25.5MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
94.0%	1	`cosTheta`
94.0%	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)))))`
94.0%	1	`(+.f32 #s(literal 1 binary32) c)`
94.0%	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))))`
94.0%	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)))`
94.0%	1	`c`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes12.0ms (0.1%)

Memory

-18.5MiB live, 22.6MiB 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:

5.0ms	c
1.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
1.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
4.7%	1	`cosTheta`
4.7%	1	`c`
4.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
4.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
4.7%	1	`(+.f32 #s(literal 1 binary32) c)`
4.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

simplify10.0ms (0.1%)

Memory

24.7MiB live, 24.8MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary32`
18×	`+-commutative_binary32`
12×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	187
1	92	187
2	101	187
3	105	187
4	106	187

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.2s (9.3%)

Memory

14.8MiB live, 1 086.3MiB allocated

Rules

9 656×	`accelerator-lowering-fma.f32`
9 656×	`accelerator-lowering-fma.f64`
7 048×	`accelerator-lowering-fma.f32`
7 048×	`accelerator-lowering-fma.f64`
6 886×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	276
1	294	263
2	2824	263
0	8570	247
0	18	89
1	126	80
2	1045	73
0	8542	73
0	410	3676
1	1246	3572
2	4762	3476
0	8360	3311
0	993	11062
1	3403	10418
0	8185	10005
0	45	294
1	321	263
2	2797	263
0	9852	244
0	1183	16075
1	3925	15574
0	8568	14879
0	49	338
1	323	326
2	2846	326
0	8726	308

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 447 to 247 computations (44.7% saved)

preprocess89.0ms (0.7%)

Memory: 5.2MiB live, 196.0MiB allocated
Compiler: Compiled 432 to 164 computations (62% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze28.0ms (0.2%)

sample2.0s (15.6%)

preprocess260.0ms (2%)

explain505.0ms (4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify221.0ms (1.7%)

localize113.0ms (0.9%)

series28.0ms (0.2%)

rewrite579.0ms (4.6%)

simplify394.0ms (3.1%)

eval67.0ms (0.5%)

prune101.0ms (0.8%)

simplify295.0ms (2.3%)

localize156.0ms (1.2%)

series73.0ms (0.6%)

rewrite493.0ms (3.9%)

simplify620.0ms (4.9%)

eval264.0ms (2.1%)

prune299.0ms (2.4%)

simplify207.0ms (1.6%)

localize139.0ms (1.1%)

series44.0ms (0.3%)

rewrite313.0ms (2.5%)

simplify438.0ms (3.4%)

eval245.0ms (1.9%)

prune269.0ms (2.1%)

simplify276.0ms (2.2%)

localize153.0ms (1.2%)

series62.0ms (0.5%)

rewrite799.0ms (6.3%)

simplify429.0ms (3.4%)

eval301.0ms (2.4%)

prune412.0ms (3.2%)

regimes189.0ms (1.5%)

regimes149.0ms (1.2%)

regimes134.0ms (1.1%)

regimes114.0ms (0.9%)

regimes90.0ms (0.7%)

regimes61.0ms (0.5%)

regimes51.0ms (0.4%)

regimes23.0ms (0.2%)

regimes24.0ms (0.2%)

regimes13.0ms (0.1%)

regimes12.0ms (0.1%)

regimes12.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.2s (9.3%)

preprocess89.0ms (0.7%)

end0.0ms (0%)

Profiling