Metrics for Beckmann Sample, normalization factor

analyze28.0ms (0.2%)

Memory

-16.1MiB live, 61.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample2.1s (15.3%)

Memory

58.2MiB live, 3 133.3MiB allocated

Samples

1.5s	8 256×	0	valid
10.0ms	70×	0	invalid

Precisions

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

ival-div: 257.0ms (21.6% of total)

const: 171.0ms (14.4% of total)

ival-sqrt: 149.0ms (12.5% of total)

ival-mult: 143.0ms (12% of total)

ival-<: 91.0ms (7.7% of total)

ival-exp: 86.0ms (7.2% of total)

ival-add: 82.0ms (6.9% of total)

ival-sub: 76.0ms (6.4% of total)

ival-pi: 51.0ms (4.3% of total)

ival-neg: 44.0ms (3.7% of total)

ival-and: 22.0ms (1.9% of total)

exact: 14.0ms (1.2% of total)

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

Bogosity

preprocess282.0ms (2%)

Memory

8.2MiB live, 168.4MiB allocated

Algorithm

1×	egg-herbie

Rules

1 608×	`accelerator-lowering-fma.f32`
1 608×	`accelerator-lowering-fma.f64`
1 466×	`div-sub`
1 040×	`-lowering-.f32`
1 040×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	127
1	135	117
2	394	111
3	1316	110
4	3697	110
5	5276	110
6	7001	110
7	7750	110
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)))

explain300.0ms (2.1%)

Memory

8.4MiB live, 525.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
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)))))`
0	-	-	`(sqrt.f32 (PI.f32))`
0	-	-	`(PI.f32)`
0	-	-	`(*.f32 (neg.f32 cosTheta) cosTheta)`
0	-	-	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) 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) 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 #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)))))`	n/o	1	0
↳	`(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)`	overflow	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)))`	overflow	1
↳	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`	overflow	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))))`	overflow	1

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

68.0ms

512×

valid

Compiler

Compiled 310 to 76 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 12.0ms (25.4% of total)

ival-div: 10.0ms (21.1% of total)

ival-sqrt: 7.0ms (14.8% of total)

ival-add: 5.0ms (10.6% of total)

ival-exp: 4.0ms (8.5% of total)

ival-sub: 4.0ms (8.5% of total)

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

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

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0%)

Memory

-36.1MiB live, 3.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

98.0%

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

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify163.0ms (1.2%)

Memory

17.9MiB live, 175.8MiB 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)

localize87.0ms (0.6%)

Memory

-50.1MiB live, 144.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	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

47.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-sqrt: 13.0ms (34.7% of total)

ival-div: 11.0ms (29.4% of total)

ival-mult: 4.0ms (10.7% of total)

ival-add: 3.0ms (8% of total)

ival-sub: 3.0ms (8% of total)

ival-exp: 2.0ms (5.3% of total)

ival-pi: 1.0ms (2.7% of total)

ival-neg: 1.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series43.0ms (0.3%)

Memory

3.4MiB live, 43.0MiB allocated

Counts

6 → 84

Calls

Call 1

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

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

Calls

21 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
3.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
2.0ms	cosTheta	@	inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
2.0ms	cosTheta	@	-inf	(* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
1.0ms	cosTheta	@	-inf	(* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))

rewrite306.0ms (2.2%)

Memory

23.7MiB live, 816.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 473

Calls

Call 1

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

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

simplify454.0ms (3.2%)

Memory

-3.1MiB live, 701.9MiB 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))

eval71.0ms (0.5%)

Memory: 34.4MiB live, 151.8MiB allocated
Compiler: Compiled 23 196 to 2 836 computations (87.8% saved)

prune104.0ms (0.7%)

Memory

-38.4MiB live, 250.8MiB allocated

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	531	26	557
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	532	26	558

Accuracy

99.9%

Counts

558 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) cosTheta) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
▶	98.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c)))
▶	98.0%	(/.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)))
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (.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) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	97.8%	(/.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)))
	57.8%	(/.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)))
	97.9%	(/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.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 #s(literal 1 binary32) c)) cosTheta) (*.f32 cosTheta (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
▶	93.9%	(/.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))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) c) cosTheta)) cosTheta))
	96.2%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	91.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	98.0%	(/.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)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.2%	(/.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)))
	95.4%	(/.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)))
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta)))))
	93.9%	(/.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)))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta)))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.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) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.6%	(/.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)))))
▶	5.1%	(/.f32 #s(literal 1 binary32) c)
	94.7%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	92.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 204 to 768 computations (36.2% saved)

simplify228.0ms (1.6%)

Memory

27.1MiB live, 259.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.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))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	cost-diff	64	(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta)
✓	cost-diff	192	(/.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)))
✓	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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c)))
✓	cost-diff	192	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
✓	cost-diff	192	(fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c))

Rules

4 320×	`accelerator-lowering-fma.f32`
4 320×	`accelerator-lowering-fma.f64`
3 352×	`-lowering-.f32`
3 352×	`-lowering-.f64`
2 206×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	405
1	91	405
2	196	403
3	388	391
4	837	391
5	2050	391
6	5126	391
0	8592	367

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c)))
1
(+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c))
(/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI)))
(/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(cbrt (PI))
(PI)
(/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))
(exp (* cosTheta (neg cosTheta)))
(* cosTheta (neg cosTheta))
(neg cosTheta)
(pow (PI) 1/6)
1/6
(+ 1 c)
c
(/ 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 (+ (+ 1 c) (/ (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (sqrt (PI)))))
1
(+ (+ 1 c) (/ (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (sqrt (PI))))
(+ 1 c)
c
(/ (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (sqrt (PI)))
(/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta)
(* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta))))
(sqrt (- (- 1 cosTheta) cosTheta))
(- (- 1 cosTheta) cosTheta)
(- 1 cosTheta)
cosTheta
(exp (* cosTheta (neg cosTheta)))
(* cosTheta (neg cosTheta))
(neg cosTheta)
(sqrt (PI))
(PI)

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

localize166.0ms (1.2%)

Memory

1.8MiB live, 295.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta)
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.0%	(/.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)))
✓	accuracy	98.9%	(/.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)))))
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	98.9%	(/.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	98.1%	(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	97.6%	(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
✓	accuracy	98.2%	(/.f32 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
✓	accuracy	96.9%	(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.3%	(fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.0%	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (cbrt.f32 (PI.f32))) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (+.f32 #s(literal 1 binary32) c)))

Samples

98.0ms

256×

valid

Compiler

Compiled 395 to 45 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-div: 21.0ms (34.6% of total)

ival-mult: 8.0ms (13.2% of total)

ival-sqrt: 7.0ms (11.5% of total)

ival-add: 6.0ms (9.9% of total)

ival-pow: 5.0ms (8.2% of total)

ival-sub: 4.0ms (6.6% of total)

const: 4.0ms (6.6% of total)

ival-exp: 2.0ms (3.3% of total)

ival-cbrt: 2.0ms (3.3% 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)

series123.0ms (0.9%)

Memory

-24.7MiB live, 206.5MiB allocated

Counts

21 → 348

Calls

Call 1

Inputs
#<alt (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c))>
#<alt (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI)))>
#<alt (/ 1 (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c)))>
#<alt (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)>
#<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 (/ (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (sqrt (PI)))>
#<alt (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta)>
#<alt (/ 1 (+ (+ 1 c) (/ (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (sqrt (PI)))))>
#<alt (+ (+ 1 c) (/ (/ (* (sqrt (- (- 1 cosTheta) cosTheta)) (exp (* cosTheta (neg cosTheta)))) cosTheta) (sqrt (PI))))>
#<alt (- (- 1 cosTheta) cosTheta)>
#<alt (sqrt (/ 1 (PI)))>
#<alt (sqrt (/ (+ (* cosTheta -2) 1) (PI)))>
#<alt (/ (+ (* cosTheta -2) 1) (PI))>

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

87 calls:

Time	Variable		Point	Expression
55.0ms	cosTheta	@	0	(+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c))
12.0ms	c	@	0	(+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c))
3.0ms	cosTheta	@	inf	(/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI)))
2.0ms	cosTheta	@	-inf	(/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI)))
1.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (cbrt (PI))) (/ (exp (* cosTheta (neg cosTheta))) (pow (PI) 1/6))) (+ 1 c)))

rewrite358.0ms (2.6%)

Memory

12.8MiB live, 720.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 888×	`/-lowering-/.f32`
3 888×	`/-lowering-/.f64`
3 296×	`-lowering-.f32`
3 296×	`-lowering-.f64`
2 664×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	294
1	300	268
2	3015	263
0	8844	250

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1 020

Calls

Call 1

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

Outputs
(exp.f32 (neg.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) c)) #s(literal -1 binary32))))
(+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) c))
(+.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) (+.f32 #s(literal 1 binary32) c))
(+.f32 c (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)))
(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)))
(+.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)) c)
(+.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) c) #s(literal 1 binary32))
(pow.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 3 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 3 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (-.f32 (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) (+.f32 #s(literal 1 binary32) c))
(fma.f32 #s(literal 1 binary32) c (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)))
(fma.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (exp.f32 (-.f32 (-.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 #s(literal 1/6 binary32) (log.f32 (PI.f32)))) (*.f32 (log.f32 (PI.f32)) #s(literal 1/3 binary32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (*.f32 cosTheta (cbrt.f32 (PI.f32))))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal -1/6 binary32))) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (*.f32 cosTheta (cbrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 c #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (neg.f32 cosTheta)) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (fma.f32 c (.f32 c c) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 c (-.f32 c #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)))
(fma.f32 (-.f32 #s(literal 1 binary32) (.f32 c c)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) c)) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)))
(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (*.f32 cosTheta (cbrt.f32 (PI.f32)))) (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (pow.f32 (PI.f32) #s(literal 1/12 binary32))) (exp.f32 (-.f32 (neg.f32 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 (PI.f32)) #s(literal 1/12 binary32)))) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c))
(fma.f32 (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) (neg.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (neg.f32 cosTheta)) (+.f32 #s(literal 1 binary32) c))
(-.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)))) (/.f32 (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)))))
(-.f32 (/.f32 (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32)) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c)))) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (+.f32 #s(literal 1 binary32) c) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (-.f32 (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) #s(literal 2 binary32)) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (fma.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta)) (fma.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (neg.f32 (+.f32 #s(literal 1 binary32) c))) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (fma.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta)) #s(literal 3 binary32))))))
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(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))
(/.f32 (neg.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32))) (neg.f32 (PI.f32)))
(/.f32 (neg.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (neg.f32 (cbrt.f32 (PI.f32))))
(sqrt.f32 (*.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)))
(*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) (PI.f32)))
(.f32 (.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -2/3 binary32)) (pow.f32 (/.f32 (cbrt.f32 (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (PI.f32) (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(.f32 (pow.f32 (/.f32 (PI.f32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))

simplify484.0ms (3.5%)

Memory

15.2MiB live, 930.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 226×	`accelerator-lowering-fma.f32`
9 226×	`accelerator-lowering-fma.f64`
7 064×	`-lowering-.f32`
7 064×	`-lowering-.f64`
3 956×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	831	12566
1	2626	12165
0	8275	11652

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

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

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

eval159.0ms (1.1%)

Memory: 30.6MiB live, 372.7MiB allocated
Compiler: Compiled 53 024 to 4 758 computations (91% saved)

prune237.0ms (1.7%)

Memory

1.4MiB live, 368.3MiB allocated

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	1 488	22	1 510
Fresh	14	7	21
Picked	4	1	5
Done	0	0	0
Total	1 506	30	1 536

Accuracy

100.0%

Counts

1 536 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.6%	(/.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))
	94.1%	(/.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)))))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	96.3%	(/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (*.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) c)))
	97.7%	(/.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)))
	94.3%	(/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (neg.f32 (.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)))
▶	94.4%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
	91.2%	(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	93.8%	(/.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))
	91.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	93.8%	(/.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)))))))
	98.0%	(/.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)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal -3/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
	94.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta)))))
	91.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
▶	93.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	53.9%	(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))
✓	5.1%	(/.f32 #s(literal 1 binary32) c)
	94.9%	(.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)))))
	94.7%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
▶	92.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 353 to 828 computations (38.8% saved)

simplify292.0ms (2.1%)

Memory

-7.2MiB live, 546.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(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))))
✓	cost-diff	96	(/.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)))) (*.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	352	(/.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 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
✓	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	0	(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	(/.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	256	(/.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	448	(/.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	(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
✓	cost-diff	64	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
✓	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 #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

10 006×	`accelerator-lowering-fma.f32`
10 006×	`accelerator-lowering-fma.f64`
4 006×	`+-lowering-+.f64`
4 006×	`+-lowering-+.f32`
2 244×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	493
1	120	493
2	370	489
3	1656	476
4	5979	476
0	8245	448

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

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

localize208.0ms (1.5%)

Memory

15.8MiB live, 250.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.5%	(*.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	98.4%	(/.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)))) (*.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	97.2%	(+.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	98.2%	(/.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	97.2%	(+.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	99.6%	(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
✓	accuracy	98.2%	(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) 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 #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	98.9%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

76.0ms

256×

valid

Compiler

Compiled 492 to 46 computations (90.7% saved)

Precisions

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

ival-div: 17.0ms (31.6% of total)

ival-mult: 14.0ms (26.1% of total)

ival-add: 10.0ms (18.6% of total)

ival-sqrt: 5.0ms (9.3% of total)

ival-exp: 2.0ms (3.7% of total)

ival-sub: 2.0ms (3.7% of total)

ival-neg: 2.0ms (3.7% of total)

ival-pi: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series75.0ms (0.5%)

Memory

-19.0MiB live, 135.2MiB allocated

Counts

27 → 420

Calls

Call 1

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

Calls

105 calls:

Time	Variable		Point	Expression
19.0ms	c	@	inf	(* cosTheta (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))
5.0ms	c	@	0	(/ 1 (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (* cosTheta (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))))
3.0ms	cosTheta	@	-inf	(+ (+ 1 c) (/ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) cosTheta))
2.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (/ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) cosTheta)))
2.0ms	c	@	-inf	(/ 1 (/ (+ (* cosTheta (* (+ 1 (+ c (/ -1 (sqrt (PI))))) (+ cosTheta (* cosTheta (+ c (/ -1 (sqrt (PI)))))))) (neg (/ 1 (PI)))) (* cosTheta (+ (* cosTheta (+ 1 (+ c (/ -1 (sqrt (PI)))))) (/ -1 (sqrt (PI)))))))

rewrite714.0ms (5.1%)

Memory

-145.1MiB live, 804.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 604×	`/-lowering-/.f32`
3 604×	`/-lowering-/.f64`
3 506×	`-lowering-.f32`
3 506×	`-lowering-.f64`
3 066×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	320
1	325	285
2	3289	285
0	9040	274

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 1 334

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

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

simplify727.0ms (5.2%)

Memory

-14.5MiB live, 801.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6 580×	`accelerator-lowering-fma.f32`
6 580×	`accelerator-lowering-fma.f64`
6 104×	`-lowering-.f32`
6 104×	`-lowering-.f64`
4 582×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1028	14928
1	3409	13681
0	8158	13191

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

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

eval487.0ms (3.5%)

Memory: 45.2MiB live, 538.9MiB allocated
Compiler: Compiled 104 103 to 9 566 computations (90.8% saved)

prune570.0ms (4.1%)

Memory

-9.3MiB live, 596.4MiB allocated

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	2 668	11	2 679
Fresh	6	18	24
Picked	4	1	5
Done	0	1	1
Total	2 678	31	2 709

Accuracy

100.0%

Counts

2 709 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.6%	(/.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))
	94.1%	(/.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)))))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
▶	96.3%	(/.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)))
	94.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (*.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) c)))
	97.7%	(/.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)))
	94.3%	(/.f32 #s(literal 1 binary32) (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)))
	94.3%	(/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (neg.f32 (.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)))
	94.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
	94.2%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
	91.2%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	98.0%	(/.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)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal -3/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
	94.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta)))))
	91.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	53.8%	(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
	93.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.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)))))
✓	5.1%	(/.f32 #s(literal 1 binary32) c)
▶	94.7%	(*.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))))
▶	91.8%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	92.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1 173 to 785 computations (33.1% saved)

simplify380.0ms (2.7%)

Memory

6.5MiB live, 295.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

7 554×	`accelerator-lowering-fma.f32`
7 554×	`accelerator-lowering-fma.f64`
2 902×	`-lowering-.f32`
2 902×	`-lowering-.f64`
1 692×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	285
1	98	279
2	213	279
3	575	276
4	1705	270
5	5387	270
0	8279	254

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize282.0ms (2%)

Memory

-32.8MiB live, 241.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	100.0%	(E.f32)
✓	accuracy	98.9%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	accuracy	96.9%	(log.f32 (E.f32))
✓	accuracy	99.8%	(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
✓	accuracy	98.9%	(/.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))) (+.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	97.6%	(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	97.2%	(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	99.1%	(/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
✓	accuracy	98.9%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) 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 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.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	98.9%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Samples

169.0ms

256×

valid

Compiler

Compiled 285 to 46 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-sqrt: 53.0ms (37.7% of total)

ival-mult: 48.0ms (34.2% of total)

ival-div: 20.0ms (14.2% of total)

ival-add: 7.0ms (5% of total)

ival-sub: 4.0ms (2.8% of total)

ival-log: 3.0ms (2.1% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series81.0ms (0.6%)

Memory

22.9MiB live, 99.6MiB allocated

Counts

27 → 288

Calls

Call 1

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

Outputs
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)>
#<alt (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))>
#<alt (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
#<alt (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))>
#<alt (* 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))))))>
#<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 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 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 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 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 (* -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 (* -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 (* -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 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))))) (* (sqrt 2) (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))))) (pow cosTheta 6))) (/ 1 (+ 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 (* -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 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))))))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)>
#<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))))))))))))) cosTheta)>
#<alt (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))>
#<alt (+ 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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#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)>
#<alt (* -1 (* (sqrt (/ (pow cosTheta 3) (PI))) (sqrt -2)))>
#<alt (* (pow cosTheta 2) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))))))>
#<alt (* (sqrt (/ (pow cosTheta 3) (PI))) (* (sqrt -1) (sqrt 2)))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (pow cosTheta 2))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5))))) (pow cosTheta 6))) (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))))))>
#<alt (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))>
#<alt (+ 1 (+ c (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))>
#<alt (+ 1 (+ c (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))>
#<alt c>
#<alt (* c (+ 1 (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt (* c (+ 1 (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))>
#<alt 1>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))>
#<alt (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))>
#<alt (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))>
#<alt (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))>
#<alt (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (* (PI) (log (E)))))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt 1>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (+ 1 (* -2 cosTheta))>
#<alt (* -2 cosTheta)>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* cosTheta (- (/ 1 cosTheta) 2))>
#<alt (* -2 cosTheta)>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))>
#<alt (* -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 (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 (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))))))>

Calls

72 calls:

Time	Variable		Point	Expression
35.0ms	cosTheta	@	0	(* cosTheta (sqrt (* (PI) (log (E)))))
13.0ms	c	@	-inf	(/ 1 (+ (* (/ (+ (* cosTheta (neg cosTheta)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
3.0ms	cosTheta	@	-inf	(/ 1 (+ (* (/ (+ (* cosTheta (neg cosTheta)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))
3.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
3.0ms	cosTheta	@	inf	(/ 1 (+ (* (/ (+ (* cosTheta (neg cosTheta)) 1) cosTheta) (sqrt (/ (+ (* cosTheta -2) 1) (PI)))) (+ 1 c)))

rewrite578.0ms (4.1%)

Memory

2.3MiB live, 808.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 084×	`-lowering-.f32`
5 084×	`-lowering-.f64`
3 972×	`accelerator-lowering-fma.f32`
3 972×	`accelerator-lowering-fma.f64`
2 588×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	230
1	291	214
2	2434	214
0	8149	203

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 1 118

Calls

Call 1

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

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 (.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 (.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 (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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))))) (.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) cosTheta)
(/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) #s(literal 1 binary32)) (*.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 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (exp.f32 (.f32 cosTheta (neg.f32 cosTheta)))) (sqrt.f32 (PI.f32))) cosTheta)
(.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 (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 (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 (/.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 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))) #s(literal 1 binary32))
(.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 (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)) #s(literal 1 binary32)) (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.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))))
(.f32 (/.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 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)))) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) (.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))) #s(literal 1 binary32))))
(exp.f32 (.f32 (log1p.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (*.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))) #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))) #s(literal 1 binary32)) #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))) #s(literal 1 binary32)))) #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))) #s(literal 1 binary32)) #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))) #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))) #s(literal 1 binary32))) #s(literal -1/2 binary32))
(pow.f32 (exp.f32 (log1p.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))))))) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (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)))
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(/.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))) #s(literal 1 binary32))))
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(/.f32 (sqrt.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal -1 binary32))) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (-.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal 1 binary32)) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 (sqrt.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32))) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(*.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))
(*.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(*.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32)))))
(*.f32 (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)) (pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)))
(.f32 (pow.f32 (.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(.f32 (sqrt.f32 (.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(neg.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (neg.f32 (PI.f32))))
(neg.f32 (/.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (PI.f32)))
(exp.f32 (*.f32 (log.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(literal -1 binary32)))
(exp.f32 (fma.f32 (log.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1/2 binary32) (*.f32 (log.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1/2 binary32))))
(pow.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1 binary32))
(pow.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 2 binary32))
(pow.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (*.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) #s(literal 1/2 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal 1 binary32)))
(/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))
(/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) #s(literal 1 binary32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (neg.f32 (PI.f32)))
(/.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) (.f32 (PI.f32) (-.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal 1 binary32)) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal 1 binary32)) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))
(/.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) #s(literal -1 binary32)) (.f32 (-.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal 1 binary32)) (.f32 cosTheta #s(literal -2 binary32))) (neg.f32 (PI.f32))))
(/.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)) (PI.f32)))
(/.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) #s(literal -1 binary32)) (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)) (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (neg.f32 (neg.f32 (PI.f32))))
(/.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) (PI.f32))
(/.f32 (*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal -1 binary32)) (neg.f32 (PI.f32)))
(/.f32 (.f32 (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal 1 binary32)) (*.f32 cosTheta #s(literal -2 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32)))
(/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) (PI.f32))
(/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(/.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(sqrt.f32 (*.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)) (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32)))
(*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (pow.f32 (/.f32 (sqrt.f32 (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)))
(*.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))))
(*.f32 (neg.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))))
(.f32 (.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (/.f32 (cbrt.f32 (PI.f32)) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (PI.f32) (fma.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32) #s(literal 1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal 1 binary32)) (*.f32 cosTheta #s(literal -2 binary32)))))
(.f32 (pow.f32 (/.f32 (PI.f32) (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))
(E.f32)
(exp.f32 #s(literal 1 binary32))
(exp.f32 (*.f32 (log.f32 (exp.f32 #s(literal 1/3 binary32))) #s(literal 3 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (E.f32) (*.f32 (E.f32) (E.f32)))) #s(literal 1/3 binary32)))
(exp.f32 (*.f32 (log.f32 (sqrt.f32 (E.f32))) #s(literal 2 binary32)))
(fabs.f32 (E.f32))
(pow.f32 (E.f32) #s(literal 1 binary32))
(pow.f32 (exp.f32 #s(literal 1/3 binary32)) #s(literal 3 binary32))
(pow.f32 (*.f32 (E.f32) (E.f32)) #s(literal 1/2 binary32))
(pow.f32 (.f32 (E.f32) (.f32 (E.f32) (E.f32))) #s(literal 1/3 binary32))
(pow.f32 (sqrt.f32 (E.f32)) #s(literal 2 binary32))
(sqrt.f32 (*.f32 (E.f32) (E.f32)))
(cbrt.f32 (.f32 (E.f32) (.f32 (E.f32) (E.f32))))
(*.f32 #s(literal 1 binary32) (E.f32))
(*.f32 (E.f32) #s(literal 1 binary32))
(*.f32 (exp.f32 #s(literal 1/3 binary32)) (pow.f32 (E.f32) #s(literal 2/3 binary32)))
(*.f32 (exp.f32 #s(literal 1/3 binary32)) (log.f32 (exp.f32 (pow.f32 (E.f32) #s(literal 2/3 binary32)))))
(*.f32 (exp.f32 #s(literal 1/3 binary32)) (sqrt.f32 (pow.f32 (E.f32) #s(literal 4/3 binary32))))
(*.f32 (pow.f32 (E.f32) #s(literal 2/3 binary32)) (exp.f32 #s(literal 1/3 binary32)))
(*.f32 (pow.f32 (E.f32) #s(literal 2/3 binary32)) (pow.f32 (pow.f32 (E.f32) #s(literal 1/6 binary32)) #s(literal 2 binary32)))
(*.f32 (sqrt.f32 (E.f32)) (sqrt.f32 (E.f32)))
(*.f32 (sqrt.f32 (E.f32)) (log.f32 (exp.f32 (sqrt.f32 (E.f32)))))
(.f32 (sqrt.f32 (sqrt.f32 (E.f32))) (sqrt.f32 (.f32 (E.f32) (sqrt.f32 (E.f32)))))
(*.f32 (pow.f32 (cbrt.f32 (pow.f32 (E.f32) #s(literal 2/3 binary32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (exp.f32 #s(literal 1/3 binary32))) #s(literal 3 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (E.f32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (sqrt.f32 (E.f32))) #s(literal 3 binary32)))
(.f32 (pow.f32 (.f32 (E.f32) (sqrt.f32 (E.f32))) #s(literal 1/3 binary32)) (pow.f32 (*.f32 (E.f32) (sqrt.f32 (E.f32))) #s(literal 1/3 binary32)))
(.f32 (pow.f32 (.f32 (*.f32 (E.f32) (E.f32)) (pow.f32 (E.f32) #s(literal 2/3 binary32))) #s(literal 1/3 binary32)) (cbrt.f32 (exp.f32 #s(literal 1/3 binary32))))
(.f32 (pow.f32 (.f32 (*.f32 (E.f32) (E.f32)) (sqrt.f32 (E.f32))) #s(literal 1/3 binary32)) (cbrt.f32 (sqrt.f32 (E.f32))))
(.f32 (cbrt.f32 (.f32 (E.f32) (sqrt.f32 (E.f32)))) (cbrt.f32 (*.f32 (E.f32) (sqrt.f32 (E.f32)))))
(.f32 (cbrt.f32 (.f32 (*.f32 (E.f32) (E.f32)) (pow.f32 (E.f32) #s(literal 2/3 binary32)))) (cbrt.f32 (exp.f32 #s(literal 1/3 binary32))))
(.f32 (cbrt.f32 (.f32 (*.f32 (E.f32) (E.f32)) (sqrt.f32 (E.f32)))) (cbrt.f32 (sqrt.f32 (E.f32))))
(.f32 (sqrt.f32 (.f32 (E.f32) (sqrt.f32 (E.f32)))) (sqrt.f32 (sqrt.f32 (E.f32))))
(.f32 (sqrt.f32 (cbrt.f32 (.f32 (.f32 (E.f32) (E.f32)) (.f32 (E.f32) (E.f32))))) (exp.f32 #s(literal 1/3 binary32)))
(.f32 (sqrt.f32 (.f32 (E.f32) (pow.f32 (E.f32) #s(literal 2/3 binary32)))) (pow.f32 (E.f32) #s(literal 1/6 binary32)))
(log.f32 (exp.f32 (E.f32)))

simplify500.0ms (3.6%)

Memory

-6.7MiB live, 1 100.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 526×	`accelerator-lowering-fma.f32`
11 526×	`accelerator-lowering-fma.f64`
8 170×	`-lowering-.f32`
8 170×	`-lowering-.f64`
4 920×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	730	7689
1	2442	7212
0	8337	6940

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

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)))))))
(* 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)))))
(+ (* -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))))))
(- (+ (* -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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(* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))
(/ (+ (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2))) (/ (* (PI) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))) (* cosTheta (pow (sqrt 2) 2)))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (sqrt -1) (pow (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))) 2)) (pow (sqrt 2) 3)))) (/ (* cosTheta (* (PI) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))))) (pow (sqrt 2) 2))) (pow cosTheta 4))) (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* -1 (/ (* (PI) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))) (* cosTheta (pow (sqrt 2) 2))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (* cosTheta (PI))) (/ (* (sqrt -1) (* (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))) (+ (* -1 (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (sqrt -1) (pow (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))) 2)) (pow (sqrt 2) 3)))) (/ (* cosTheta (* (PI) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))))) (pow (sqrt 2) 2))))) (sqrt 2)))) (+ (* (sqrt (* (pow cosTheta 3) (pow (PI) 3))) (/ (* (sqrt -1) (* (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))))) (pow (sqrt 2) 3))) (/ (* cosTheta (* (PI) (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5))))))) (pow (sqrt 2) 2)))) (pow cosTheta 6))) (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1 (* (sqrt (/ (pow (PI) 3) (pow cosTheta 5))) (/ (* (sqrt -1) (pow (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))) 2)) (pow (sqrt 2) 3)))) (+ (* -1 (/ (* (PI) (+ 1 (+ c (* -1 (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))) (* cosTheta (pow (sqrt 2) 2)))) (/ (* (PI) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))))) (* (pow cosTheta 3) (pow (sqrt 2) 2)))))) (pow cosTheta 2))
(/ 1 (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(* -1 (* (sqrt (/ (pow cosTheta 3) (PI))) (sqrt -2)))
(* (pow cosTheta 2) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))
(* (pow cosTheta 2) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))))
(* (pow cosTheta 2) (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))))))
(* (sqrt (/ (pow cosTheta 3) (PI))) (* (sqrt -1) (sqrt 2)))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (pow cosTheta 2))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5))))) (pow cosTheta 6))) (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))))))
(+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (+ 1 (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
1
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (* -1 (pow cosTheta 2)))
(* -1 (pow cosTheta 2))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(* -1 (pow cosTheta 2))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (* (PI) (log (E)))))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
(* cosTheta (sqrt (PI)))
1
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(+ 1 (* -2 cosTheta))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* cosTheta (- (/ 1 cosTheta) 2))
(* -2 cosTheta)
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(* -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)))
(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))))))

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

eval262.0ms (1.9%)

Memory: 36.4MiB live, 702.5MiB allocated
Compiler: Compiled 50 706 to 6 616 computations (87% saved)

prune281.0ms (2%)

Memory

-17.5MiB live, 842.6MiB allocated

Pruning

43 alts after pruning (38 fresh and 5 done)

	Pruned	Kept	Total
New	1 793	21	1 814
Fresh	7	17	24
Picked	2	3	5
Done	0	2	2
Total	1 802	43	1 845

Accuracy

100.0%

Counts

1 845 → 43

Alt Table

Click to see full alt table

Status	Accuracy	Program
	94.7%	(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))))
	96.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (*.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)))
	97.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	97.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	96.1%	(/.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))) #s(literal 1 binary32)))
	96.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #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)))
	94.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	97.7%	(/.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))) #s(literal 1 binary32)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (*.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) c)))
	94.3%	(/.f32 #s(literal 1 binary32) (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)))
	94.3%	(/.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)))
	98.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (neg.f32 (.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)))
	94.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
	54.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 (+.f32 cosTheta (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.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)))
	91.2%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
	94.2%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
	93.8%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
✓	91.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
	98.0%	(/.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)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal -3/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
	94.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta)))))
	93.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.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)))))
✓	5.1%	(/.f32 #s(literal 1 binary32) c)
	91.6%	(*.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
	56.5%	(.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))))
	94.7%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) c (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	91.6%	(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) c (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	94.6%	(*.f32 cosTheta (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	92.0%	(.f32 cosTheta (fma.f32 (.f32 (PI.f32) c) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
	94.1%	(.f32 cosTheta (.f32 (fma.f32 cosTheta (PI.f32) (/.f32 (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (neg.f32 c))) (neg.f32 c)))
	93.7%	(.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)))))
✓	91.8%	(.f32 cosTheta (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
✓	92.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	94.0%	(.f32 c (fma.f32 cosTheta (/.f32 (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) c) (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))))))

Compiler

Compiled 2 388 to 888 computations (62.8% saved)

regimes152.0ms (1.1%)

Memory

7.7MiB live, 396.4MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

28.0ms	c
27.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
26.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
25.0ms	(.f32 (.f32 (/.f32 #s(literal 1 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	cosTheta

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`c`
98.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.4%	1	`(+.f32 #s(literal 1 binary32) c)`
98.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes140.0ms (1%)

Memory

-9.6MiB live, 354.5MiB allocated

Counts

80 → 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 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) c (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (neg.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 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (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)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #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) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (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 (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 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal -3/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
(.f32 cosTheta (.f32 (fma.f32 cosTheta (PI.f32) (/.f32 (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (neg.f32 c))) (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) (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 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) c) (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (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 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (*.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)))
(/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 (+.f32 cosTheta (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.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 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 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 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #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) (/.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) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (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 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 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 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
(.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 #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) (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 #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))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (*.f32 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 (.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 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (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) (fma.f32 (.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) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (neg.f32 (.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 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.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) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (+.f32 cosTheta cosTheta))) cosTheta) (/.f32 (exp.f32 (*.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (PI.f32))) (+.f32 #s(literal 1 binary32) c)))
(/.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 #s(literal 1 binary32) (fma.f32 (/.f32 (exp.f32 (.f32 cosTheta (neg.f32 cosTheta))) cosTheta) (sqrt.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32) #s(literal -1 binary32)) (*.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal -1 binary32))))) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (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 (.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 #s(literal 1 binary32) c)) cosTheta) (*.f32 cosTheta (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (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) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(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)))))

Outputs

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

Calls

6 calls:

26.0ms	(.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)))
24.0ms	c
23.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
22.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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	cosTheta

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`c`
98.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.4%	1	`(+.f32 #s(literal 1 binary32) c)`
98.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes153.0ms (1.1%)

Memory

-16.8MiB live, 181.5MiB allocated

Counts

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

Calls

6 calls:

48.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
26.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
20.0ms	c
19.0ms	(/.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	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes114.0ms (0.8%)

Memory

17.1MiB live, 176.6MiB allocated

Counts

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

Outputs

(/.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)))

Calls

6 calls:

21.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
20.0ms	c
20.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
19.0ms	cosTheta
17.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes111.0ms (0.8%)

Memory

-5.8MiB live, 149.0MiB 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 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (sqrt.f32 (PI.f32)))))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) c (-.f32 (PI.f32) (sqrt.f32 (PI.f32)))) (neg.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 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (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)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 (fma.f32 (PI.f32) (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #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) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (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 (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 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta #s(literal -3/2 binary32) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
(.f32 cosTheta (.f32 (fma.f32 cosTheta (PI.f32) (/.f32 (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (neg.f32 c))) (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) (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 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) c) (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))))))
(/.f32 #s(literal 1 binary32) (+.f32 c (fma.f32 c (/.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (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 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (fma.f32 cosTheta (fma.f32 cosTheta (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (*.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)))
(/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 (+.f32 cosTheta (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.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 (fma.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (.f32 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 #s(literal 1 binary32) (fma.f32 (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #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) (/.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) (fma.f32 (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -1/6 binary32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (/.f32 (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 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 cosTheta (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -1 binary32))) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (neg.f32 c)) c (neg.f32 c))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 cosTheta #s(literal 1/2 binary32) #s(literal -3/2 binary32))) (*.f32 cosTheta cosTheta))) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 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 (sqrt.f32 (.f32 (PI.f32) (log.f32 (E.f32)))))
(.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 #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) (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 #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))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 cosTheta (.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (+.f32 cosTheta (.f32 cosTheta (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))))) (neg.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (fma.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))))))

Outputs

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

Calls

6 calls:

20.0ms	cosTheta
20.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
19.0ms	c
16.0ms	(+.f32 #s(literal 1 binary32) c)
16.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
97.8%	1	`cosTheta`
97.8%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.8%	1	`(+.f32 #s(literal 1 binary32) c)`
97.8%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.8%	1	`c`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes103.0ms (0.7%)

Memory

11.9MiB live, 168.2MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

19.0ms	(/.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	c
18.0ms	cosTheta
15.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
15.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

regimes100.0ms (0.7%)

Memory

20.5MiB live, 134.6MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`cosTheta`
97.2%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.2%	1	`c`
97.2%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.2%	1	`(+.f32 #s(literal 1 binary32) c)`
97.2%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes87.0ms (0.6%)

Memory

-3.9MiB live, 113.4MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

25.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
14.0ms	c
13.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
12.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
11.0ms	cosTheta

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes76.0ms (0.5%)

Memory

-18.0MiB live, 108.2MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

18.0ms	cosTheta
13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
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	c
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)))

Results

Accuracy	Segments	Branch
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)))`
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)))))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes70.0ms (0.5%)

Memory

0.7MiB live, 116.6MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

14.0ms	cosTheta
13.0ms	c
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	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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)))))

Results

Accuracy	Segments	Branch
96.3%	1	`cosTheta`
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	`c`
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)

regimes65.0ms (0.5%)

Memory

36.2MiB live, 112.2MiB allocated

Counts

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

Outputs

(/.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)))

Calls

6 calls:

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

Results

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

Compiler

Compiled 84 to 58 computations (31% saved)

regimes91.0ms (0.6%)

Memory

-20.3MiB live, 96.7MiB allocated

Counts

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

Outputs

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

Calls

6 calls:

42.0ms	c
10.0ms	(+.f32 #s(literal 1 binary32) c)
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
9.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
95.9%	1	`cosTheta`
95.9%	1	`c`
95.9%	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)))))`
95.9%	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))))`
95.9%	1	`(+.f32 #s(literal 1 binary32) c)`
95.9%	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)

regimes67.0ms (0.5%)

Memory

-3.4MiB live, 71.6MiB allocated

Counts

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

Outputs
(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))))

Calls

6 calls:

24.0ms	(+.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
8.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	c

Results

Accuracy	Segments	Branch
94.7%	1	`cosTheta`
94.7%	1	`c`
94.7%	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)))))`
94.7%	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))))`
94.7%	1	`(+.f32 #s(literal 1 binary32) c)`
94.7%	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)

regimes52.0ms (0.4%)

Memory

-3.2MiB live, 74.7MiB allocated

Counts

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

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

Calls

6 calls:

11.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
10.0ms	c
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
8.0ms	cosTheta

Results

Accuracy	Segments	Branch
94.7%	1	`c`
94.7%	1	`(+.f32 #s(literal 1 binary32) c)`
94.7%	1	`cosTheta`
94.7%	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)))))`
94.7%	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))))`
94.7%	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)

regimes18.0ms (0.1%)

Memory

36.2MiB live, 36.2MiB allocated

Counts

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

Outputs
(*.f32 cosTheta (fma.f32 (-.f32 (PI.f32) (sqrt.f32 (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))

Calls

6 calls:

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 (.f32 (/.f32 #s(literal 1 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	cosTheta
3.0ms	c

Results

Accuracy	Segments	Branch
94.6%	1	`cosTheta`
94.6%	1	`c`
94.6%	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)))))`
94.6%	1	`(+.f32 #s(literal 1 binary32) c)`
94.6%	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))))`
94.6%	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)

regimes17.0ms (0.1%)

Memory

-7.1MiB live, 28.6MiB 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 (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)))
2.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
2.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	cosTheta
2.0ms	c

Results

Accuracy	Segments	Branch
92.0%	1	`c`
92.0%	1	`cosTheta`
92.0%	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)))))`
92.0%	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))))`
92.0%	1	`(+.f32 #s(literal 1 binary32) c)`
92.0%	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)

regimes10.0ms (0.1%)

Memory

-16.4MiB live, 21.9MiB 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:

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)))))
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	c
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
5.1%	1	`cosTheta`
5.1%	1	`c`
5.1%	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)))))`
5.1%	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))))`
5.1%	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)))`
5.1%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 84 to 58 computations (31% saved)

simplify12.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary32`
20×	`*-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	91	312
1	116	312
2	125	312
3	130	312
4	132	312

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (9.3%)

Memory

6.8MiB live, 1 226.7MiB allocated

Rules

11 526×	`accelerator-lowering-fma.f32`
11 526×	`accelerator-lowering-fma.f64`
9 656×	`accelerator-lowering-fma.f32`
9 656×	`accelerator-lowering-fma.f64`
9 226×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	831	12566
1	2626	12165
0	8275	11652
0	730	7689
1	2442	7212
0	8337	6940
0	44	230
1	291	214
2	2434	214
0	8149	203
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	1028	14928
1	3409	13681
0	8158	13191

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

Compiler

Compiled 627 to 304 computations (51.5% saved)

preprocess114.0ms (0.8%)

Memory: 5.3MiB live, 177.0MiB allocated
Compiler: Compiled 682 to 212 computations (68.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze28.0ms (0.2%)

sample2.1s (15.3%)

preprocess282.0ms (2%)

explain300.0ms (2.1%)

eval0.0ms (0%)

prune2.0ms (0%)

simplify163.0ms (1.2%)

localize87.0ms (0.6%)

series43.0ms (0.3%)

rewrite306.0ms (2.2%)

simplify454.0ms (3.2%)

eval71.0ms (0.5%)

prune104.0ms (0.7%)

simplify228.0ms (1.6%)

localize166.0ms (1.2%)

series123.0ms (0.9%)

rewrite358.0ms (2.6%)

simplify484.0ms (3.5%)

eval159.0ms (1.1%)

prune237.0ms (1.7%)

simplify292.0ms (2.1%)

localize208.0ms (1.5%)

series75.0ms (0.5%)

rewrite714.0ms (5.1%)

simplify727.0ms (5.2%)

eval487.0ms (3.5%)

prune570.0ms (4.1%)

simplify380.0ms (2.7%)

localize282.0ms (2%)

series81.0ms (0.6%)

rewrite578.0ms (4.1%)

simplify500.0ms (3.6%)

eval262.0ms (1.9%)

prune281.0ms (2%)

regimes152.0ms (1.1%)

regimes140.0ms (1%)

regimes153.0ms (1.1%)

regimes114.0ms (0.8%)

regimes111.0ms (0.8%)

regimes103.0ms (0.7%)

regimes100.0ms (0.7%)

regimes87.0ms (0.6%)

regimes76.0ms (0.5%)

regimes70.0ms (0.5%)

regimes65.0ms (0.5%)

regimes91.0ms (0.6%)

regimes67.0ms (0.5%)

regimes52.0ms (0.4%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes10.0ms (0.1%)

simplify12.0ms (0.1%)

soundness1.3s (9.3%)

preprocess114.0ms (0.8%)

end0.0ms (0%)

Profiling