Metrics for Beckmann Sample, normalization factor

analyze42.0ms (0.3%)

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 42 to 28 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-<: 5.0ms (17.9% of total)

ival-div: 4.0ms (14.3% of total)

ival-mult: 4.0ms (14.3% of total)

...c/correct-round.rkt:119:19: 3.0ms (10.7% of total)

ival-sqrt: 3.0ms (10.7% of total)

ival-add: 2.0ms (7.2% of total)

ival-exp: 2.0ms (7.2% of total)

ival-sub: 2.0ms (7.2% of total)

ival-pi: 1.0ms (3.6% of total)

ival-and: 1.0ms (3.6% of total)

ival-neg: 1.0ms (3.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample2.4s (14.8%)

Results

1.9s	8256×	0	valid
10.0ms	59×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-div: 530.0ms (34.5% of total)

ival-mult: 164.0ms (10.7% of total)

...c/correct-round.rkt:119:19: 151.0ms (9.8% of total)

ival-sqrt: 140.0ms (9.1% of total)

ival-<: 138.0ms (9% of total)

ival-add: 100.0ms (6.5% of total)

ival-sub: 85.0ms (5.5% of total)

ival-exp: 79.0ms (5.1% of total)

ival-neg: 48.0ms (3.1% of total)

ival-pi: 42.0ms (2.7% of total)

ival-and: 39.0ms (2.5% of total)

const: 16.0ms (1% of total)

backward-pass: 4.0ms (0.3% of total)

Bogosity

preprocess246.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

1866×	`fma-define`
1660×	`sum5-define`
1336×	`fnmadd-define`
1216×	`sum4-define`
1108×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	132
1	160	122
2	468	115
3	1634	108
4	5081	108
5	7566	108
0	18	21
1	53	20
2	123	19
3	290	18
4	475	18
5	1045	18
6	2713	18
7	4306	18
8	5827	18
9	7315	18
0	8020	18

Stop Event

1×	iter limit
1×	node limit
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) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) (*.f32 (exp.f32 (*.f32 cosTheta cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))))

Call 2

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

Outputs
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(recip (fma (/ (sqrt (fma cosTheta -2 1)) cosTheta) (/ (fast-isqrt (PI)) (fast-exp (square cosTheta))) (+ 1 c)))
(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 (neg cosTheta)) (neg cosTheta))) (neg cosTheta))) (exp (* (neg (neg cosTheta)) (neg cosTheta))))))
(recip (fnmadd (/ (sqrt (sum3 1 cosTheta cosTheta)) cosTheta) (/ (fast-isqrt (PI)) (fast-exp (square cosTheta))) (+ 1 c)))
(/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(recip (fma (fast-isqrt (PI)) (/ (sqrt (fma cosTheta -2 1)) (* (fast-exp (square cosTheta)) cosTheta)) (- 1 c)))
(neg (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 (neg cosTheta)) (neg cosTheta))) (neg cosTheta))) (exp (* (neg (neg cosTheta)) (neg cosTheta)))))))
(recip (- -1 (fnmadd (/ (sqrt (sum3 1 cosTheta cosTheta)) cosTheta) (/ (fast-isqrt (PI)) (fast-exp (square cosTheta))) c)))
(neg (/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))))
(recip (fnmsub (fast-isqrt (PI)) (/ (sqrt (fma cosTheta -2 1)) (* (fast-exp (square cosTheta)) cosTheta)) (- 1 c)))
(/ 1 (+ (+ 1 cosTheta) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 c) c)) c)) (exp (* (neg c) c)))))
(recip (fma (/ (sqrt (fma c -2 1)) c) (/ (fast-isqrt (PI)) (fast-exp (square c))) (+ 1 cosTheta)))

explain274.0ms (1.7%)

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

Results

153.0ms

512×

valid

Compiler

Compiled 285 to 56 computations (80.4% saved)

Precisions

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

ival-sqrt: 15.0ms (26.5% of total)

ival-div: 11.0ms (19.5% of total)

ival-mult: 9.0ms (15.9% of total)

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

ival-exp: 5.0ms (8.8% of total)

ival-sub: 5.0ms (8.8% of total)

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

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

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 24 to 17 computations (29.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))

Status

Accuracy

Program

▶

97.6%

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

▶

98.1%

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

Compiler

Compiled 51 to 35 computations (31.4% saved)

simplify155.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 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 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) 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	0	(/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
✓	cost-diff	0	(+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))

Rules

1946×	`fma-define`
1432×	`fnmadd-define`
1216×	`sum4-define`
1108×	`fma-lowering-fma.f32`
1108×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	216
1	81	201
2	176	198
3	352	198
4	534	198
5	1132	198
6	2918	198
7	4449	198
8	6056	198
9	7476	198
0	8181	198

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize210.0ms (1.3%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.2%	(*.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)))
✓	accuracy	99.9%	(.f32 (exp.f32 (.f32 cosTheta cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	accuracy	99.0%	(/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
✓	accuracy	98.7%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)

Results

161.0ms

256×

valid

Compiler

Compiled 246 to 31 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-sub: 27.0ms (38.1% of total)

ival-mult: 16.0ms (22.6% of total)

ival-div: 8.0ms (11.3% of total)

ival-add: 6.0ms (8.5% of total)

ival-sqrt: 6.0ms (8.5% of total)

ival-exp: 5.0ms (7% of total)

ival-pi: 1.0ms (1.4% of total)

const: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

backward-pass: 0.0ms (0% of total)

series53.0ms (0.3%)

Counts

12 → 192

Calls

Call 1

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

48 calls:

Time	Variable		Point	Expression
8.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
5.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (+ c (/ (sqrt (+ 1 (* cosTheta -2))) (* (exp (* cosTheta cosTheta)) (* (sqrt (PI)) cosTheta))))))
5.0ms	cosTheta	@	inf	(/ 1 (+ 1 (+ c (/ (sqrt (+ 1 (* cosTheta -2))) (* (exp (* cosTheta cosTheta)) (* (sqrt (PI)) cosTheta))))))
4.0ms	c	@	0	(+ 1 (+ c (/ (sqrt (+ 1 (* cosTheta -2))) (* (exp (* cosTheta cosTheta)) (* (sqrt (PI)) cosTheta)))))
3.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))

rewrite494.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4860×	`-lowering-.f32`
4860×	`-lowering-.f64`
2588×	`/-lowering-/.f32`
2588×	`/-lowering-/.f64`
2370×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	156
1	212	150
2	1878	146
0	9135	146

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 662

Calls

Call 1

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

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

simplify380.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

6454×	`-lowering-.f32`
6454×	`-lowering-.f64`
3646×	`+-lowering-+.f64`
3646×	`+-lowering-+.f32`
1818×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	7288
1	2226	6404
0	8541	6404

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval148.0ms (0.9%)

Compiler: Compiled 38564 to 4041 computations (89.5% saved)

prune147.0ms (0.9%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	828	26	854
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	829	27	856

Accuracy

99.9%

Counts

856 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	58.7%	(pow.f32 (.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c))) #s(literal -1/2 binary32))
▶	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
	91.4%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)) c))
	94.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32)))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) c)))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))))
	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	58.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (*.f32 cosTheta c)))))))
	10.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	58.6%	(/.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
▶	5.1%	(/.f32 #s(literal 1 binary32) c)
	58.5%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) #s(literal 2 binary32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))))))
	34.7%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (pow.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) #s(literal 3 binary32)))) (+.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (-.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)))))
	95.4%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
	92.4%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.3%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (.f32 cosTheta cosTheta)))))) #s(literal -1 binary32)))

Compiler

Compiled 1324 to 821 computations (38% saved)

simplify193.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	cost-diff	0	(+.f32 c (/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	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) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta 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) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
✓	cost-diff	32	(.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))
✓	cost-diff	0	(+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
✓	cost-diff	32	(+.f32 (neg.f32 cosTheta) #s(literal 1 binary32))
✓	cost-diff	64	(/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) 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 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	32	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta)))

Rules

1996×	`sum3-define`
1612×	`sum5-define`
1264×	`fnmsub-define`
1168×	`fma-define`
1142×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	50	437
1	134	401
2	271	386
3	634	386
4	1381	386
5	2506	386
6	5098	385
7	7627	385
0	8219	385

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize395.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta)
✓	accuracy	99.8%	(/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	accuracy	98.7%	(/.f32 (/.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	99.8%	(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
✓	accuracy	98.4%	(/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32)))
✓	accuracy	99.6%	(*.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
✓	accuracy	98.3%	(/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) (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%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.9%	(/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta)))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.3%	(/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) #s(literal 1/2 binary32)) cosTheta))

Results

243.0ms

256×

valid

Compiler

Compiled 505 to 51 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-pow: 26.0ms (27.8% of total)

ival-div: 24.0ms (25.7% of total)

ival-mult: 13.0ms (13.9% of total)

ival-add: 12.0ms (12.8% of total)

ival-exp: 7.0ms (7.5% of total)

ival-sqrt: 4.0ms (4.3% of total)

ival-pi: 3.0ms (3.2% of total)

ival-neg: 3.0ms (3.2% of total)

ival-sub: 1.0ms (1.1% of total)

const: 1.0ms (1.1% of total)

backward-pass: 0.0ms (0% of total)

series60.0ms (0.4%)

Counts

26 → 420

Calls

Call 1

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

Calls

105 calls:

Time	Variable		Point	Expression
11.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (* (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))
3.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (* (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))
3.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (/ (* (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))
2.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (* (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) (exp (neg (* cosTheta cosTheta)))) cosTheta)))
2.0ms	cosTheta	@	inf	(/ (pow (+ 1 (* cosTheta -2)) 1/2) (exp (* cosTheta cosTheta)))

rewrite466.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3170×	`-lowering-.f32`
3170×	`-lowering-.f64`
1942×	`fma-lowering-fma.f32`
1942×	`fma-lowering-fma.f64`
1718×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	336
1	370	275
2	3526	272
0	8275	272

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 1052

Calls

Call 1

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

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

simplify474.0ms (3%)

Algorithm

1×	egg-herbie

Rules

5254×	`-lowering-.f32`
5254×	`-lowering-.f64`
3156×	`+-lowering-+.f64`
3156×	`+-lowering-+.f32`
1678×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1305	13972
1	4747	12636
0	8632	12636

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

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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/ (+ (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 cosTheta (-.f32 (.f32 (*.f32 cosTheta #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 #s(literal -1/2 binary32) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+.f32 (+.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))) (.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)))))
(+ (* -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 (.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)))) (+.f32 (+.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))) (.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))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 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))))))
(+.f32 (-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 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)))))))
(+.f32 (-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (+.f32 (.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)))))) (.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)))))))
(* (/ 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -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))) (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 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 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (+.f32 (.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))))))) (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 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta)))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.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 (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (neg.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) 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)))))
(-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (*.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)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+.f32 (-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (*.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)))))))
(+.f32 (-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (+.f32 (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (.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 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta))))
(+ (* -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) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))) (/.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #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)))))))
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(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
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(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
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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 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (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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(- (+ (* -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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(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))) (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (+.f32 (.f32 (neg.f32 (.f32 cosTheta (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
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(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
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(/ -1 (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1))
(/.f32 #s(literal -1 binary32) (+.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal -1 binary32)))
(- (* -1 (* (/ 1 (* cosTheta (pow (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1) 2))) (sqrt (/ 1 (PI))))) (/ 1 (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1)))
(-.f32 (neg.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (pow.f32 (+.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal -1 binary32)) #s(literal 2 binary32))))) (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal -1 binary32))))
(- (* -1 (/ (- (/ 1 (* cosTheta (* (PI) (pow (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1) 3)))) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1) 2))))) cosTheta)) (/ 1 (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1)))
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(- (* -1 (/ (- (* -1 (/ (- (* -1 (* (/ 1 (* cosTheta (pow (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1) 2))))) cosTheta)) (/ 1 (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1)))
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(/ cosTheta (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))))
(/.f32 cosTheta (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1 (/ (* c (pow cosTheta 2)) (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 2))) (/ cosTheta (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))))
(-.f32 (/.f32 cosTheta (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 (.f32 (.f32 cosTheta cosTheta) c) (pow.f32 (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) #s(literal 2 binary32))))
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(+ (* c (- (* c (- (* -1 (/ (* c (pow cosTheta 4)) (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 4))) (* -1 (/ (pow cosTheta 3) (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 3))))) (/ (pow cosTheta 2) (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 2)))) (/ cosTheta (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))))
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) c)) c)
(/ (- (+ 1 (/ (* (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))) (* (pow c 2) cosTheta))) (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))) c)
(/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (.f32 (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (.f32 cosTheta (.f32 c c))) (+.f32 (/.f32 #s(literal 1 binary32) c) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c))))) c)
(/ (- (+ 1 (* -1 (/ (* (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 2)) (* (pow c 3) (pow cosTheta 2))))) (+ (* -1 (/ (* (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))) (* (pow c 2) cosTheta))) (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
(/.f32 (+.f32 (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (* (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))) (* c cosTheta)) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (.f32 (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (.f32 cosTheta c)) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (* (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 2)) (* c (pow cosTheta 2))) (/ (* (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))) cosTheta)) c)) (+ 1 (* (/ (- 1 cosTheta) 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))))))))
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(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
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(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
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(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
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(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* -1 c)) 1)))
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(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (+ (* -1 c) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) 1)))
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(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (+ (* -1 c) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) 1)))
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(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (+ (* -1 c) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) 1)))
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(+ cosTheta (+ (* c cosTheta) (* (sqrt (/ 1 (PI))) (- 1 cosTheta))))
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(+ cosTheta (+ (* c cosTheta) (* (sqrt (/ 1 (PI))) (- 1 cosTheta))))
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(* c cosTheta)
(*.f32 cosTheta c)
(* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))
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(* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))
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(* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))
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(* c cosTheta)
(*.f32 cosTheta c)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))
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(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))
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(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))
(.f32 (neg.f32 c) (-.f32 (neg.f32 cosTheta) (/.f32 (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) c)))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))
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(+ (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))))))))))))
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(* (sqrt (/ cosTheta (PI))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))
(.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta)))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(.f32 cosTheta (+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))))
(.f32 cosTheta (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.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 (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)) (exp.f32 (*.f32 cosTheta cosTheta))))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(neg.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (+.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.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 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.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 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (+.f32 (+.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))) (.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 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta)))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))))))))
(/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))) (/.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 2 binary32))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
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(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta))) c)) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 2 binary32)) (.f32 c c)) (+.f32 (/.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta c)))))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 3 binary32)) (.f32 c (.f32 c c)))) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta c)))) (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 2 binary32)) (*.f32 c c)))) c)
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(/.f32 (+.f32 (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta c))) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 2 binary32)) c) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta)))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 3 binary32)) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) cosTheta))) #s(literal 2 binary32))) (neg.f32 c)) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) cosTheta)))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (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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c
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c
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -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))) (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 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 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (+.f32 (.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))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))
(/.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (sqrt.f32 #s(literal -2 binary32))) (exp.f32 (.f32 cosTheta cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))
(/.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (neg.f32 (exp.f32 (*.f32 cosTheta cosTheta))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))))
(-.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (/.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (exp.f32 (*.f32 cosTheta cosTheta))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3)))))))
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(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 5))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))))))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (sqrt (PI)))))
(.f32 cosTheta (.f32 (+.f32 cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* -1/2 (* (* cosTheta (+ (PI) (* -4 (PI)))) (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 cosTheta (.f32 #s(literal -3 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (sqrt (PI)) (* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (PI))) (+ (PI) (* -4 (PI))))) (* -1/2 (* (* cosTheta (+ (* -8 (PI)) (* -1 (+ (PI) (* -4 (PI)))))) (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 #s(literal -1/2 binary32) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3 binary32) (PI.f32))) (.f32 cosTheta (.f32 (+.f32 (.f32 (PI.f32) #s(literal -8 binary32)) (.f32 #s(literal 3 binary32) (PI.f32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))))))
(* (sqrt (* cosTheta (PI))) (sqrt -1/2))
(.f32 (sqrt.f32 (.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1/2 binary32)))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))
(.f32 cosTheta (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (*.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 (PI.f32) cosTheta)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2)))))
(.f32 cosTheta (+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (.f32 #s(literal -1/16 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -1/2 binary32))))) (.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 (PI.f32) cosTheta)))))
(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (+ (* 1/64 (/ (* cosTheta (PI)) (pow (sqrt -1/2) 2))) (* 1/16 (PI))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -1/2))))))
(.f32 cosTheta (+.f32 (+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (.f32 #s(literal -1/16 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -1/2 binary32))))) (.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 (PI.f32) cosTheta)))) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32)))))) (/.f32 (+.f32 (/.f32 (.f32 #s(literal 1/64 binary32) (.f32 cosTheta (PI.f32))) #s(literal -1/2 binary32)) (.f32 (PI.f32) #s(literal 1/16 binary32))) (sqrt.f32 #s(literal -1/2 binary32))))))
(* (sqrt (* cosTheta (PI))) (* (sqrt -1) (sqrt 1/2)))
(.f32 (.f32 (sqrt.f32 (*.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32)))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32)))) (.f32 (sqrt.f32 (/.f32 (PI.f32) cosTheta)) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(.f32 (neg.f32 cosTheta) (-.f32 (+.f32 (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32)))) (.f32 #s(literal 1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 (sqrt.f32 (/.f32 (PI.f32) cosTheta)) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ (PI) cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (+ (* -1/64 (/ (* cosTheta (PI)) (pow (sqrt 1/2) 2))) (* 1/16 (PI)))) (sqrt 1/2)))) (* -1/16 (* (sqrt (* cosTheta (PI))) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(.f32 (neg.f32 cosTheta) (-.f32 (-.f32 (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32)))) (/.f32 (+.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)))) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (+.f32 (.f32 (PI.f32) #s(literal 1/16 binary32)) (/.f32 (.f32 #s(literal -1/64 binary32) (.f32 cosTheta (PI.f32))) #s(literal 1/2 binary32)))) (sqrt.f32 #s(literal 1/2 binary32)))) (.f32 (.f32 #s(literal -1/16 binary32) (sqrt.f32 (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 (/.f32 (PI.f32) cosTheta)) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))))
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -1/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -1/2 binary32)) #s(literal -1/2 binary32))) #s(literal -1 binary32)))) cosTheta)
(* (sqrt (/ 1 cosTheta)) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))
(+.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -2 binary32)))))
(+ (* -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))))
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(+ (* -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)))))
(+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (+.f32 (+.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -2 binary32))))) (*.f32 #s(literal 1/16 binary32) (/.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))))))
(* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))
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(*.f32 cosTheta (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(*.f32 cosTheta (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(*.f32 cosTheta (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) 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 (/.f32 #s(literal -1 binary32) cosTheta) (PI.f32))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(*.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) (PI.f32))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(*.f32 (neg.f32 cosTheta) (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal -1 binary32) cosTheta) (PI.f32))))
1
#s(literal 1 binary32)
(+ 1 (* -1 cosTheta))
(-.f32 #s(literal 1 binary32) cosTheta)
(+ 1 (* cosTheta (- (* -3/2 cosTheta) 1)))
(+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32))))
(+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1)))
(+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32))))
(* (sqrt cosTheta) (/ (sqrt -2) (exp (pow cosTheta 2))))
(.f32 (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 cosTheta))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2))))))
(.f32 cosTheta (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 cosTheta cosTheta)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2)))))))
(.f32 cosTheta (+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 cosTheta cosTheta)))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2))))))))
(.f32 cosTheta (+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (.f32 (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (*.f32 cosTheta cosTheta))))))
(* -1 (* (sqrt cosTheta) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))
(neg.f32 (/.f32 (.f32 (sqrt.f32 cosTheta) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (exp.f32 (*.f32 cosTheta cosTheta))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 #s(literal -1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (*.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (.f32 #s(literal 1/16 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))))) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))))
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta)
(* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2))))
(/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 cosTheta cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2)))))
(+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (*.f32 cosTheta cosTheta))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2))))))
(+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 cosTheta cosTheta)))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta cosTheta))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 cosTheta)) (/ (sqrt -2) (exp (pow cosTheta 2)))))))
(+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (.f32 (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 cosTheta cosTheta)))))
(* -1 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))
(neg.f32 (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))))
(-.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3)))))))
(+.f32 (-.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 #s(literal 1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 5))))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))))))
(+.f32 (-.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (+.f32 (.f32 #s(literal 1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))) (exp.f32 (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (.f32 #s(literal -1/16 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))))))

eval269.0ms (1.7%)

Compiler: Compiled 51773 to 4753 computations (90.8% saved)

prune174.0ms (1.1%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	1481	20	1501
Fresh	12	9	21
Picked	4	1	5
Done	1	0	1
Total	1498	30	1528

Accuracy

100.0%

Counts

1528 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.2%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
	94.7%	(/.f32 cosTheta (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))
	94.9%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) cosTheta))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) cosTheta))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) cosTheta))
	93.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 c (+.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) c)) (/.f32 cosTheta c)))) cosTheta))
	91.4%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)) c))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta)))
	94.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	55.5%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)))) #s(literal 1 binary32)))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	91.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	10.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	94.5%	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))))
✓	5.1%	(/.f32 #s(literal 1 binary32) c)
	95.8%	(.f32 (/.f32 cosTheta (+.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (pow.f32 (+.f32 (.f32 cosTheta c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) #s(literal 3 binary32)))) (+.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 (.f32 cosTheta c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (-.f32 (+.f32 (.f32 cosTheta c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) cosTheta))))
	58.5%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (pow.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))) #s(literal 2 binary32)))) (-.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))))))
	95.4%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
	92.4%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.3%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))

Compiler

Compiled 1291 to 834 computations (35.4% saved)

simplify192.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
✓	cost-diff	0	(+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	cost-diff	64	(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
✓	cost-diff	0	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	cost-diff	0	(+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32))
✓	cost-diff	0	(+.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)) c))
✓	cost-diff	64	(.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))

Rules

1994×	`fma-lowering-fma.f32`
1994×	`fma-lowering-fma.f64`
1974×	`sum3-define`
1946×	`fmsub-define`
1936×	`fnmadd-define`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	48	373
1	122	349
2	227	343
3	319	342
4	488	342
5	797	342
6	1542	332
7	3730	332
0	8526	332

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize539.0ms (3.4%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))
✓	accuracy	99.9%	(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
✓	accuracy	99.8%	(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	accuracy	98.7%	(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	100.0%	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	accuracy	99.9%	(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	accuracy	98.7%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	100.0%	(+.f32 #s(literal 1 binary32) c)
✓	accuracy	99.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.8%	(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) #s(literal 1 binary32)) c))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta)
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32)))

Results

438.0ms

256×

valid

Compiler

Compiled 420 to 49 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-div: 26.0ms (35.9% of total)

ival-add: 15.0ms (20.7% of total)

ival-mult: 12.0ms (16.6% of total)

ival-pow: 6.0ms (8.3% of total)

ival-exp: 5.0ms (6.9% of total)

ival-sqrt: 4.0ms (5.5% of total)

ival-pi: 1.0ms (1.4% of total)

ival-sub: 1.0ms (1.4% of total)

const: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

backward-pass: 0.0ms (0% of total)

series40.0ms (0.3%)

Counts

25 → 420

Calls

Call 1

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

105 calls:

Time	Variable		Point	Expression
6.0ms	cosTheta	@	inf	(+ (+ (* (/ (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) cosTheta) (exp (neg (* cosTheta cosTheta)))) 1) c)
1.0ms	cosTheta	@	inf	(/ 1 (+ 1 (+ c (/ (/ (+ 1 (* cosTheta (+ (* cosTheta -3/2) -1))) cosTheta) (pow (PI) 1/2)))))
1.0ms	c	@	0	(/ 1 (+ 1 (+ c (/ (/ (+ 1 (* cosTheta (+ (* cosTheta -3/2) -1))) cosTheta) (pow (PI) 1/2)))))
1.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (+ c (/ (/ (+ 1 (* cosTheta (+ (* cosTheta -3/2) -1))) cosTheta) (pow (PI) 1/2)))))
1.0ms	c	@	0	(+ 1 (+ c (/ (/ (+ 1 (* cosTheta (+ (* cosTheta -3/2) -1))) cosTheta) (pow (PI) 1/2))))

rewrite358.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3146×	`fma-lowering-fma.f32`
3146×	`fma-lowering-fma.f64`
2058×	`+-lowering-+.f64`
2058×	`+-lowering-+.f32`
2044×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	289
1	368	260
2	3654	260
0	8479	260

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 741

Calls

Call 1

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

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

simplify445.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

5856×	`-lowering-.f32`
5856×	`-lowering-.f64`
4390×	`+-lowering-+.f64`
4390×	`+-lowering-+.f32`
1736×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1102	11423
1	3766	10441
0	8934	10441

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 (neg (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))
(+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))
(+ 1 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))))
(+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))
1
(+ 1 (* -1 c))
(+ 1 (* c (- c 1)))
(+ 1 (* c (- (* c (+ 1 (* -1 c))) 1)))
(/ 1 c)
(/ (- 1 (/ 1 c)) c)
(/ (- (+ 1 (/ 1 (pow c 2))) (/ 1 c)) c)
(/ (- (+ 1 (/ 1 (pow c 2))) (+ (/ 1 c) (/ 1 (pow c 3)))) c)
(/ 1 c)
(* -1 (/ (- (/ 1 c) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ 1 c) 1) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 c) 1) c)) 1) c)) 1) c))
1
(+ 1 c)
(+ 1 c)
(+ 1 c)
c
(* c (+ 1 (/ 1 c)))
(* c (+ 1 (/ 1 c)))
(* c (+ 1 (/ 1 c)))
c
(* c (+ 1 (/ 1 c)))
(* c (+ 1 (/ 1 c)))
(* c (+ 1 (/ 1 c)))
(/ 1 (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))))
(+ (* -1 (/ c (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 2))) (/ 1 (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))))
(+ (* c (- (/ c (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 3)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 2)))) (/ 1 (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 3)))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 2)))) (/ 1 (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 2) (pow c 2))) (+ (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 2) (pow c 2))) (+ (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) 2) c) (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))) c)) 1) c))
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c
(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (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)))) (/ (sqrt -2) (exp (pow cosTheta 2))))))
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(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3)))))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 5))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))))))))
(* (/ 1 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)))) (/ (sqrt -2) (exp (pow cosTheta 2))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3)))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 5))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))))))
(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 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 (PI))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(* -2 (/ cosTheta (PI)))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* -2 (/ cosTheta (PI)))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
-1
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
-1
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
(- (/ 1 cosTheta) 1)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* -1 (* cosTheta (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 cosTheta)
(* cosTheta (- (* -3/2 cosTheta) 1))
(* cosTheta (- (* -3/2 cosTheta) 1))
(* cosTheta (- (* -3/2 cosTheta) 1))
(* -3/2 (pow cosTheta 2))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(* -3/2 (pow cosTheta 2))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 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))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.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 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 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)
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(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
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c
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c
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(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (+.f32 (.f32 (neg.f32 (.f32 cosTheta (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))
(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
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(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
(-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))))) (/.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 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))
(/ 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)))))))))
(+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32)))) (-.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 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (/.f32 (+.f32 (neg.f32 (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (*.f32 cosTheta (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 4 binary32))))) cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))) cosTheta))
(+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))
(+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
c
(* c (+ 1 (+ (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) c))) #s(literal 1 binary32))
(* c (+ 1 (+ (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) c))) #s(literal 1 binary32))
(* c (+ 1 (+ (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) c))) #s(literal 1 binary32))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) c)) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) c)) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))) c)) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (neg.f32 c)) #s(literal -1 binary32)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ 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))))))
(-.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)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (* (sqrt (/ 1 (PI))) (- (/ 1 cosTheta) 1)))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
c
(* c (+ 1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))))
(.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) c)))
(* c (+ 1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))))
(.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) c)))
(* c (+ 1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))))
(.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) c)))
c
(* -1 (* c (- (* -1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (* (/ (- (/ 1 cosTheta) 1) c) (sqrt (/ 1 (PI))))) 1)))
(.f32 (neg.f32 c) (+.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (neg.f32 c)) #s(literal -1 binary32)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(+ c (* -1 (sqrt (/ 1 (PI)))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (* -1 (sqrt (/ 1 (PI)))))
(-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 c (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
(+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 c (*.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 (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 cosTheta (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 cosTheta (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 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(* -3/2 cosTheta)
(*.f32 cosTheta #s(literal -3/2 binary32))
(* -1 (* cosTheta (+ 3/2 (/ 1 cosTheta))))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) #s(literal -1 binary32))
(* cosTheta (- (/ 1 (pow cosTheta 2)) (+ 3/2 (/ 1 cosTheta))))
(.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* cosTheta (- (/ 1 (pow cosTheta 2)) (+ 3/2 (/ 1 cosTheta))))
(.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -3/2 cosTheta)
(*.f32 cosTheta #s(literal -3/2 binary32))
(* -1 (* cosTheta (+ 3/2 (/ 1 cosTheta))))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) #s(literal -1 binary32))
(* -1 (* cosTheta (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta)))))
(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)))
(* -1 (* cosTheta (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta)))))
(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)))
(/ 1 (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2))) (/ 1 (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI)))))))
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) (/.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI)))))))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) (.f32 c (+.f32 (/.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 3 binary32))) (/.f32 #s(literal -1 binary32) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2)))) (/ 1 (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI)))))))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) (.f32 c (+.f32 (.f32 c (-.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 3 binary32))) (/.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 4 binary32))))) (/.f32 #s(literal -1 binary32) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32))))))
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) c))) c)
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) c)) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))) c)
(/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32)) (.f32 c c)) (+.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c))))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 3 binary32)) (.f32 c (.f32 c c)))) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c))) (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32)) (*.f32 c c)))) c)
(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
(/.f32 (+.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta c)) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32)) c) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 3) c) (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2)) c)) (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 3 binary32)) c) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) #s(literal 2 binary32))) (neg.f32 c)) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (neg.f32 (+.f32 (.f32 cosTheta (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))) (* 3/2 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (neg.f32 (+.f32 (.f32 cosTheta (-.f32 (.f32 (.f32 #s(literal 3/2 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))))) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))))) (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* -2/3 (* (/ 1 cosTheta) (sqrt (PI))))
(*.f32 #s(literal -2/3 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/ (+ (* -2/3 (sqrt (PI))) (* -4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -2/3 binary32)) (/.f32 (.f32 (*.f32 #s(literal 4/9 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) cosTheta)
(/ (- (+ (* -1 (/ (+ (* 8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 4/9 (sqrt (PI)))) (pow cosTheta 2))) (* -2/3 (sqrt (PI)))) (* 4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)
(/.f32 (+.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -2/3 binary32)) (/.f32 (+.f32 (.f32 (.f32 #s(literal 8/27 binary32) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) (.f32 (sqrt.f32 (PI.f32)) #s(literal 4/9 binary32))) (.f32 cosTheta cosTheta))) (/.f32 (.f32 (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -4/9 binary32)) cosTheta)) cosTheta)
(/ (- (+ (* -1 (/ (+ (* 8/27 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* 2/3 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* 8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 4/9 (sqrt (PI)))))))) (pow cosTheta 3))) (* -2/3 (sqrt (PI)))) (+ (* 8/27 (* (/ (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2) (pow cosTheta 2)) (sqrt (pow (PI) 3)))) (+ (* 4/9 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (* 4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))))) cosTheta)
(/.f32 (-.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -2/3 binary32)) (/.f32 (+.f32 (.f32 (.f32 #s(literal 8/27 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 #s(literal 2/3 binary32) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (+.f32 (.f32 (.f32 #s(literal 8/27 binary32) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) (.f32 (sqrt.f32 (PI.f32)) #s(literal 4/9 binary32)))))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (.f32 #s(literal 8/27 binary32) (/.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (.f32 #s(literal 4/9 binary32) (+.f32 (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)) (/.f32 (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))))) cosTheta)
(* -2/3 (* (/ 1 cosTheta) (sqrt (PI))))
(*.f32 #s(literal -2/3 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))
(* -1 (/ (+ (* 4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)) (* 2/3 (sqrt (PI)))) cosTheta))
(/.f32 (+.f32 (/.f32 (.f32 (.f32 #s(literal 4/9 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32))) (neg.f32 cosTheta))
(* -1 (/ (+ (* -1 (/ (- (+ (* -4/9 (* (/ 1 cosTheta) (sqrt (PI)))) (* -8/27 (* (/ (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2) cosTheta) (sqrt (pow (PI) 3))))) (* 4/9 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 2/3 (sqrt (PI)))) cosTheta))
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32)) (/.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -4/9 binary32)) (+.f32 (.f32 #s(literal -8/27 binary32) (/.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) cosTheta)) (.f32 (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -4/9 binary32)))) cosTheta)) (neg.f32 cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2/3 (* (/ (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -4/9 (sqrt (PI))) (* -8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta) (sqrt (PI)))) (* 8/27 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) (+ (* -4/9 (sqrt (PI))) (* -8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)) (* 4/9 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 2/3 (sqrt (PI)))) cosTheta))
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32)) (/.f32 (+.f32 (/.f32 (+.f32 (.f32 #s(literal -2/3 binary32) (/.f32 (.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -4/9 binary32)) (.f32 (.f32 #s(literal -8/27 binary32) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (sqrt.f32 (PI.f32))) cosTheta)) (-.f32 (/.f32 (.f32 (.f32 #s(literal 8/27 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -4/9 binary32)) (.f32 (.f32 #s(literal -8/27 binary32) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))) (neg.f32 cosTheta)) (.f32 (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -4/9 binary32))) cosTheta)) (neg.f32 cosTheta))
(+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI)))))
(+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(+ 1 (+ c (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(+ 1 (+ c (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))))
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c
(* c (+ 1 (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
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c
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c
(* c (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI))))))
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c
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(/ 1 (+ 1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 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 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 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)
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(* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))
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(sqrt (/ 1 (PI)))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
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(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
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(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
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(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
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(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
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(* (/ 1 cosTheta) (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 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 #s(literal -1/2 binary32) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
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(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(.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)))))

eval129.0ms (0.8%)

Compiler: Compiled 39252 to 4080 computations (89.6% saved)

prune395.0ms (2.5%)

Pruning

44 alts after pruning (40 fresh and 4 done)

	Pruned	Kept	Total
New	1174	20	1194
Fresh	4	20	24
Picked	1	4	5
Done	1	0	1
Total	1180	44	1224

Accuracy

100.0%

Counts

1224 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.8%	(pow.f32 (pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.2%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta))
	94.7%	(/.f32 cosTheta (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))
	94.9%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) cosTheta))
	10.9%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (*.f32 c c) #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32))))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) cosTheta))
▶	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) cosTheta))
	93.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 c (+.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) c)) (/.f32 cosTheta c)))) cosTheta))
	91.4%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (+.f32 #s(literal 1 binary32) c)))
	91.5%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) c))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)) c))
✓	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	55.5%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)))) #s(literal 1 binary32)))
	55.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (PI.f32)) (.f32 c c)) (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) c))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	94.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (fma.f32 (pow.f32 cosTheta #s(literal -1/2 binary32)) (pow.f32 cosTheta #s(literal -1/2 binary32)) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	55.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta))))
	31.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	91.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	55.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))))))
✓	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	56.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	56.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))))
	94.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
✓	10.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	94.5%	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 (+.f32 #s(literal 1 binary32) c) cosTheta))))
	10.9%	(-.f32 #s(literal 1 binary32) c)
	95.8%	(.f32 (/.f32 cosTheta (+.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (pow.f32 (+.f32 (.f32 cosTheta c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) #s(literal 3 binary32)))) (+.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 (.f32 cosTheta c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (-.f32 (+.f32 (.f32 cosTheta c) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) cosTheta))))
	55.3%	(*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (pow.f32 (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) #s(literal 2 binary32)))) (-.f32 (-.f32 #s(literal 1 binary32) c) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
▶	95.4%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
	92.4%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.3%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))
	88.6%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))) (.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))) #s(literal -1 binary32)))
▶	10.9%	#s(literal 1 binary32)

Compiler

Compiled 1794 to 1187 computations (33.8% saved)

simplify190.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (PI.f32)))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (PI.f32))))
✓	cost-diff	0	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
✓	cost-diff	0	(+.f32 c (/.f32 (*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	cost-diff	96	(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)))
✓	cost-diff	0	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
✓	cost-diff	0	(+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)))
✓	cost-diff	0	(/.f32 (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) cosTheta)
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) cosTheta))
✓	cost-diff	0	(+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c))
✓	cost-diff	0	(pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32))
✓	cost-diff	64	(.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))
✓	cost-diff	6400	(pow.f32 (pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))

Rules

2014×	`-lowering-.f32`
2014×	`-lowering-.f64`
2002×	`fnmadd-define`
1358×	`sum3-define`
1070×	`sum4-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	351
1	115	343
2	293	325
3	899	319
4	3456	305
0	8363	305

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize296.0ms (1.9%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(*.f32 cosTheta (PI.f32))
✓	accuracy	98.9%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
✓	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	99.6%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
✓	accuracy	98.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	accuracy	98.7%	(/.f32 (*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	59.1%	(*.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)))
✓	accuracy	99.6%	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))
✓	accuracy	98.8%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) cosTheta))
✓	accuracy	98.3%	(/.f32 (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.3%	(pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta)
✓	accuracy	98.4%	(pow.f32 (pow.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) c)) #s(literal -1/2 binary32)) #s(literal 2 binary32))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) cosTheta)) (PI.f32)))

Results

222.0ms

256×

valid

Compiler

Compiled 392 to 47 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 117.0ms

ival-sqrt: 46.0ms (39.4% of total)

ival-div: 18.0ms (15.4% of total)

ival-pow: 14.0ms (12% of total)

ival-mult: 13.0ms (11.1% of total)

ival-add: 8.0ms (6.9% of total)

ival-sub: 7.0ms (6% of total)

ival-pi: 4.0ms (3.4% of total)

ival-exp: 3.0ms (2.6% of total)

ival-neg: 2.0ms (1.7% of total)

const: 1.0ms (0.9% of total)

backward-pass: 0.0ms (0% of total)

series68.0ms (0.4%)

Counts

23 → 360

Calls

Call 1

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

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

Calls

90 calls:

Time	Variable		Point	Expression
17.0ms	cosTheta	@	0	(/ (+ (/ 1 cosTheta) -1) cosTheta)
8.0ms	cosTheta	@	inf	(pow (+ (* (/ (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) cosTheta) (exp (neg (* cosTheta cosTheta)))) (+ 1 c)) -1/2)
5.0ms	cosTheta	@	0	(/ 1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) cosTheta))
4.0ms	cosTheta	@	-inf	(pow (+ (* (/ (sqrt (/ (- 1 (* 2 cosTheta)) (PI))) cosTheta) (exp (neg (* cosTheta cosTheta)))) (+ 1 c)) -1/2)
3.0ms	c	@	0	(/ 1 (+ 1 (+ c (/ (* (neg cosTheta) (- 3/2 (/ (+ (/ 1 cosTheta) -1) cosTheta))) (pow (PI) 1/2)))))

rewrite425.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3188×	`fma-lowering-fma.f32`
3188×	`fma-lowering-fma.f64`
2310×	`-lowering-.f32`
2310×	`-lowering-.f64`
2110×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	269
1	331	249
2	3120	237
0	8289	237

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 579

Calls

Call 1

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

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

simplify485.0ms (3%)

Algorithm

1×	egg-herbie

Rules

6124×	`-lowering-.f32`
6124×	`-lowering-.f64`
4352×	`+-lowering-+.f64`
4352×	`+-lowering-+.f32`
1372×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1012	10661
1	3555	9689
0	8539	9689

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

Outputs
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))) (neg.f32 cosTheta)) (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (.f32 (-.f32 (-.f32 (.f32 (PI.f32) (.f32 #s(literal 1/2 binary32) (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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))))) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))) (neg.f32 cosTheta)) (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))) (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32)))))) (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (pow.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))))) #s(literal 2 binary32)))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))
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c
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))) cosTheta)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))) cosTheta)) (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 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (+.f32 (.f32 (neg.f32 (.f32 cosTheta (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 3 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))
(/.f32 #s(literal -1 binary32) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32)))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(-.f32 (/.f32 #s(literal -1 binary32) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))
(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI)))))
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(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 3)))) (/ 1 (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (sqrt (/ 1 (PI)))))
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(/ -1 (- (sqrt (/ 1 (PI))) 1))
(/.f32 #s(literal -1 binary32) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -1 binary32)))
(- (* -1 (* (/ 1 (* cosTheta (pow (- (sqrt (/ 1 (PI))) 1) 2))) (sqrt (/ 1 (PI))))) (/ 1 (- (sqrt (/ 1 (PI))) 1)))
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(- (* -1 (/ (- (/ 1 (* cosTheta (* (PI) (pow (- (sqrt (/ 1 (PI))) 1) 3)))) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (- (sqrt (/ 1 (PI))) 1) 2))))) cosTheta)) (/ 1 (- (sqrt (/ 1 (PI))) 1)))
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(- (* -1 (/ (- (* -1 (/ (- (* -1 (* (/ 1 (* cosTheta (pow (- (sqrt (/ 1 (PI))) 1) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (- (sqrt (/ 1 (PI))) 1) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (- (sqrt (/ 1 (PI))) 1) 2))))) cosTheta)) (/ 1 (- (sqrt (/ 1 (PI))) 1)))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
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(* -1 (- (sqrt (/ 1 (PI))) 1))
(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (- (sqrt (/ 1 (PI))) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
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(+ (* -1 (- (sqrt (/ 1 (PI))) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
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(+ (* -1 (- (sqrt (/ 1 (PI))) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
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(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
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(* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))
(* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))
(* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))
(* -1 (* cosTheta (- (sqrt (/ 1 (PI))) 1)))
(*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) 1)))
(*.f32 (+.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) #s(literal -1 binary32)) (neg.f32 cosTheta))
(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) 1)))
(*.f32 (+.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) #s(literal -1 binary32)) (neg.f32 cosTheta))
(* -1 (* cosTheta (- (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) 1)))
(*.f32 (+.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) #s(literal -1 binary32)) (neg.f32 cosTheta))
(sqrt (/ 1 (PI)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
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(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
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(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
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(/ 1 cosTheta)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(* -3/2 cosTheta)
(*.f32 cosTheta #s(literal -3/2 binary32))
(* -1 (* cosTheta (+ 3/2 (/ 1 cosTheta))))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) #s(literal -1 binary32))
(* cosTheta (- (/ 1 (pow cosTheta 2)) (+ 3/2 (/ 1 cosTheta))))
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(* cosTheta (- (/ 1 (pow cosTheta 2)) (+ 3/2 (/ 1 cosTheta))))
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(* -3/2 cosTheta)
(*.f32 cosTheta #s(literal -3/2 binary32))
(* -1 (* cosTheta (+ 3/2 (/ 1 cosTheta))))
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(* -1 (* cosTheta (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta)))))
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(* -1 (* cosTheta (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta)))))
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(/ 1 (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))))
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(+ (* -1 (/ c (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 2))) (/ 1 (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI))))))))
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) c))) c)
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(/ (- (+ 1 (/ (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 2) (pow c 2))) (+ (* -1 (* (/ (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) c) (sqrt (/ 1 (PI))))) (/ 1 c))) c)
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(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 3) (pow c 3)))) (+ (* -1 (* (/ (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) c) (sqrt (/ 1 (PI))))) (+ (* -1 (/ (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 2) (pow c 2))) (/ 1 c)))) c)
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(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* -1 (* (/ (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) c) (sqrt (/ 1 (PI))))) (/ 1 c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 2) c) (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI))))))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 3) c) (pow (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))) 2)) c)) (+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (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 (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 (neg.f32 cosTheta) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))) (* 3/2 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (neg.f32 (+.f32 (.f32 cosTheta (-.f32 (.f32 (.f32 #s(literal 3/2 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))))) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))))) (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* -2/3 (* (/ 1 cosTheta) (sqrt (PI))))
(*.f32 #s(literal -2/3 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))
(/ (+ (* -2/3 (sqrt (PI))) (* -4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -2/3 binary32)) (/.f32 (.f32 (*.f32 #s(literal 4/9 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)) cosTheta)
(/ (- (+ (* -1 (/ (+ (* 8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 4/9 (sqrt (PI)))) (pow cosTheta 2))) (* -2/3 (sqrt (PI)))) (* 4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) cosTheta)
(/.f32 (+.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -2/3 binary32)) (/.f32 (+.f32 (.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) #s(literal 8/27 binary32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal 4/9 binary32))) (.f32 cosTheta cosTheta))) (.f32 #s(literal -4/9 binary32) (*.f32 (PI.f32) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))) cosTheta)
(/ (- (+ (* -1 (/ (+ (* 8/27 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* 2/3 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* 8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* 4/9 (sqrt (PI)))))))) (pow cosTheta 3))) (* -2/3 (sqrt (PI)))) (+ (* 8/27 (* (/ (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2) (pow cosTheta 2)) (sqrt (pow (PI) 3)))) (+ (* 4/9 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (* 4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))))) cosTheta)
(/.f32 (-.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -2/3 binary32)) (/.f32 (+.f32 (.f32 (.f32 #s(literal 8/27 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 #s(literal 2/3 binary32) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (+.f32 (.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) #s(literal 8/27 binary32)) (.f32 (sqrt.f32 (PI.f32)) #s(literal 4/9 binary32)))))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (.f32 #s(literal 8/27 binary32) (.f32 (/.f32 (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) cosTheta) (/.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) cosTheta))) (.f32 #s(literal 4/9 binary32) (+.f32 (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))))) cosTheta)
(* -2/3 (* (/ 1 cosTheta) (sqrt (PI))))
(*.f32 #s(literal -2/3 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))
(* -1 (/ (+ (* 4/9 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)) (* 2/3 (sqrt (PI)))) cosTheta))
(/.f32 (+.f32 (/.f32 (.f32 (.f32 #s(literal 4/9 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32))) (neg.f32 cosTheta))
(* -1 (/ (+ (* -1 (/ (- (+ (* -4/9 (* (/ 1 cosTheta) (sqrt (PI)))) (* -8/27 (* (/ (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2) cosTheta) (sqrt (pow (PI) 3))))) (* 4/9 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 2/3 (sqrt (PI)))) cosTheta))
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32)) (/.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -4/9 binary32)) (+.f32 (.f32 (/.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))) cosTheta) #s(literal -8/27 binary32)) (.f32 (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -4/9 binary32)))) cosTheta)) (neg.f32 cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -2/3 (* (/ (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -4/9 (sqrt (PI))) (* -8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta) (sqrt (PI)))) (* 8/27 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) (+ (* -4/9 (sqrt (PI))) (* -8/27 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)) (* 4/9 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 2/3 (sqrt (PI)))) cosTheta))
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32)) (/.f32 (+.f32 (/.f32 (+.f32 (.f32 #s(literal -2/3 binary32) (/.f32 (.f32 (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -4/9 binary32)) (.f32 (.f32 #s(literal -8/27 binary32) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (sqrt.f32 (PI.f32))) cosTheta)) (-.f32 (/.f32 (.f32 (.f32 #s(literal 8/27 binary32) (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -4/9 binary32)) (.f32 (.f32 #s(literal -8/27 binary32) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))) (neg.f32 cosTheta)) (.f32 (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) #s(literal -4/9 binary32))) cosTheta)) (neg.f32 cosTheta))
(+ 1 (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI))))))
(-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))))
(+ 1 (+ c (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))))
(+.f32 #s(literal 1 binary32) (-.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))))))
(+ 1 (+ c (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))))
(+.f32 #s(literal 1 binary32) (-.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))))))
(+ 1 (+ c (* -1 (* (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) (sqrt (/ 1 (PI)))))))
(+.f32 #s(literal 1 binary32) (-.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 3/2 binary32))) (.f32 cosTheta (/.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))))))
c
(* c (+ 1 (+ (* -1 (* (/ (* cosTheta (- (+ 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))) c) (sqrt (/ 1 (PI))))) (/ 1 c))))
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(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
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(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
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(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
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c
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
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(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
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(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ c cosTheta))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (-.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 (*.f32 #s(literal -1/2 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 cosTheta (.f32 #s(literal -1/2 binary32) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))) (PI.f32))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (+.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32)))) (*.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))) (PI.f32))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(-.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (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))))))
(+.f32 (-.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 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)))))))
(+.f32 (-.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (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 (.f32 #s(literal 1/8 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))) (.f32 #s(literal -1/16 binary32) (*.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))) (PI.f32))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 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 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (-.f32 (.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(.f32 (.f32 cosTheta #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (-.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(.f32 (.f32 cosTheta #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* -1 (* cosTheta (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 cosTheta) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -1 (* cosTheta (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(neg.f32 (.f32 cosTheta (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) cosTheta))))
(* -1 (* cosTheta (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(neg.f32 (.f32 cosTheta (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) cosTheta))))
(/ 1 (pow cosTheta 2))
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))
(/ -1 cosTheta)
(/.f32 #s(literal -1 binary32) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
(/ -1 cosTheta)
(/.f32 #s(literal -1 binary32) cosTheta)
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) (neg.f32 cosTheta))
(- 1 (sqrt (/ 1 (PI))))
(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ 1 c) (sqrt (/ 1 (PI))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ 1 c) (sqrt (/ 1 (PI))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(- (+ 1 c) (sqrt (/ 1 (PI))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
c
(* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(*.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)))
(* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(*.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)))
(* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))
(*.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) c)))
c
(* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))
(*.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))
(*.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))
(*.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))
(* cosTheta (PI))
(*.f32 cosTheta (PI.f32))

eval167.0ms (1%)

Compiler: Compiled 36843 to 4639 computations (87.4% saved)

prune213.0ms (1.3%)

Pruning

48 alts after pruning (44 fresh and 4 done)

	Pruned	Kept	Total
New	1125	20	1145
Fresh	11	24	35
Picked	4	1	5
Done	1	3	4
Total	1141	48	1189

Accuracy

100.0%

Counts

1189 → 48

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.2%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) (/.f32 #s(literal 1 binary32) cosTheta))
	94.7%	(/.f32 cosTheta (+.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	94.7%	(/.f32 cosTheta (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))
	94.9%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta)) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)) cosTheta))
	10.9%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (*.f32 c c) #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32))))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 (+.f32 #s(literal 1 binary32) c) cosTheta)) cosTheta))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta) cosTheta))
	94.6%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) cosTheta))) cosTheta))
	94.4%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))) cosTheta))
	93.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 c (+.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) c)) (/.f32 cosTheta c)))) cosTheta))
	91.4%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (+.f32 #s(literal 1 binary32) c)))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta) #s(literal 1 binary32)) c))
✓	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	55.5%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)))) #s(literal 1 binary32)))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) cosTheta)) (PI.f32))) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))) cosTheta)))
	97.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	91.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	55.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta))))
	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	91.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	55.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))))))
	56.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta cosTheta)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	51.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	56.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (.f32 (neg.f32 cosTheta) (-.f32 #s(literal 3/2 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	56.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (*.f32 (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (neg.f32 cosTheta)))))
	56.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (*.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) (/.f32 (neg.f32 cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))))
	94.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
✓	10.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	94.5%	(/.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	10.9%	(-.f32 #s(literal 1 binary32) c)
	95.8%	(.f32 (/.f32 cosTheta (-.f32 (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))))) (-.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	95.5%	(.f32 (/.f32 cosTheta (+.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))))) (+.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) cosTheta)))))
	95.5%	(*.f32 (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) cosTheta)
	95.2%	(.f32 cosTheta (-.f32 (sqrt.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3 binary32))) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
	95.3%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
	92.4%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 c (*.f32 cosTheta (PI.f32)))))
	92.4%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	10.8%	(.f32 cosTheta (neg.f32 (.f32 c (*.f32 cosTheta (PI.f32)))))
	95.3%	(.f32 c (-.f32 (/.f32 (.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) c) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))
	90.3%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))
	88.6%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))) (.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))) #s(literal -1 binary32)))
✓	10.9%	#s(literal 1 binary32)

Compiler

Compiled 2844 to 1113 computations (60.9% saved)

regimes204.0ms (1.3%)

Counts

88 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

53.0ms	cosTheta
40.0ms	c
28.0ms	(/.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)))))
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)))
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))))

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)

regimes69.0ms (0.4%)

Counts

72 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

22.0ms	c
22.0ms	cosTheta
16.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.8%	1	`cosTheta`
97.8%	1	`c`
97.8%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes60.0ms (0.4%)

Counts

63 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

19.0ms	c
16.0ms	cosTheta
15.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.8%	1	`cosTheta`
97.8%	1	`(+.f32 #s(literal 1 binary32) c)`
97.8%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes53.0ms (0.3%)

Counts

58 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

17.0ms	c
17.0ms	cosTheta
13.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.2%	1	`cosTheta`
97.2%	1	`(+.f32 #s(literal 1 binary32) c)`
97.2%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes74.0ms (0.5%)

Counts

56 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

29.0ms	cosTheta
27.0ms	c
12.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.1%	1	`cosTheta`
97.1%	1	`(+.f32 #s(literal 1 binary32) c)`
97.1%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes62.0ms (0.4%)

Counts

47 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

29.0ms	c
17.0ms	(+.f32 #s(literal 1 binary32) c)
12.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.4%	1	`cosTheta`
96.4%	1	`(+.f32 #s(literal 1 binary32) c)`
96.4%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes45.0ms (0.3%)

Counts

36 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

16.0ms	(+.f32 #s(literal 1 binary32) c)
16.0ms	cosTheta
10.0ms	c

Results

Accuracy	Segments	Branch
96.4%	1	`cosTheta`
96.4%	1	`c`
96.4%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes50.0ms (0.3%)

Counts

35 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

29.0ms	c
10.0ms	cosTheta
8.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
96.0%	1	`cosTheta`
96.0%	1	`c`
96.0%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes38.0ms (0.2%)

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

16.0ms	c
11.0ms	cosTheta
8.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
95.6%	1	`cosTheta`
95.6%	1	`c`
95.6%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes32.0ms (0.2%)

Counts

32 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	c
9.0ms	cosTheta
7.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
95.5%	1	`cosTheta`
95.5%	1	`c`
95.5%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes16.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

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

Outputs
(/.f32 cosTheta (+.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))

Calls

3 calls:

7.0ms	c
4.0ms	cosTheta
4.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes15.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	c
4.0ms	cosTheta
3.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
92.4%	1	`cosTheta`
92.4%	1	`(+.f32 #s(literal 1 binary32) c)`
92.4%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(+.f32 #s(literal 1 binary32) c)
3.0ms	c
3.0ms	cosTheta

Results

Accuracy	Segments	Branch
92.4%	1	`c`
92.4%	1	`(+.f32 #s(literal 1 binary32) c)`
92.4%	1	`cosTheta`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes8.0ms (0%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	cosTheta
3.0ms	c
2.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
10.9%	1	`c`
10.9%	1	`(+.f32 #s(literal 1 binary32) c)`
10.9%	1	`cosTheta`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes8.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)

Outputs
#s(literal 1 binary32)

Calls

2 calls:

6.0ms	cosTheta
1.0ms	c

Results

Accuracy	Segments	Branch
10.9%	1	`c`
10.9%	1	`cosTheta`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

72×	`+-commutative_binary32`
50×	`*-commutative_binary32`
24×	`sub-neg_binary32`
16×	`neg-sub0_binary32`
16×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	234
1	154	234
2	179	234
3	197	234
4	206	234
5	209	234
6	210	234

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness4.7s (29.3%)

Rules

6454×	`-lowering-.f32`
6454×	`-lowering-.f64`
6124×	`-lowering-.f32`
6124×	`-lowering-.f64`
5856×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	269
1	331	249
2	3120	237
0	8289	237
0	30	156
1	212	150
2	1878	146
0	9135	146
0	673	7288
1	2226	6404
0	8541	6404
0	1012	10661
1	3555	9689
0	8539	9689
0	48	289
1	368	260
2	3654	260
0	8479	260
0	18	21
1	53	20
2	123	19
3	290	18
4	475	18
5	1045	18
6	2713	18
7	4306	18
8	5827	18
9	7315	18
0	8020	18
0	1305	13972
1	4747	12636
0	8632	12636
0	1102	11423
1	3766	10441
0	8934	10441

Stop Event

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

Compiler

Compiled 574 to 350 computations (39% saved)

preprocess66.0ms (0.4%)

Compiler: Compiled 528 to 216 computations (59.1% saved)

analyze42.0ms (0.3%)

sample2.4s (14.8%)

preprocess246.0ms (1.5%)

explain274.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify155.0ms (1%)

localize210.0ms (1.3%)

series53.0ms (0.3%)

rewrite494.0ms (3.1%)

simplify380.0ms (2.4%)

eval148.0ms (0.9%)

prune147.0ms (0.9%)

simplify193.0ms (1.2%)

localize395.0ms (2.5%)

series60.0ms (0.4%)

rewrite466.0ms (2.9%)

simplify474.0ms (3%)

eval269.0ms (1.7%)

prune174.0ms (1.1%)

simplify192.0ms (1.2%)

localize539.0ms (3.4%)

series40.0ms (0.3%)

rewrite358.0ms (2.2%)

simplify445.0ms (2.8%)

eval129.0ms (0.8%)

prune395.0ms (2.5%)

simplify190.0ms (1.2%)

localize296.0ms (1.9%)

series68.0ms (0.4%)

rewrite425.0ms (2.7%)

simplify485.0ms (3%)

eval167.0ms (1%)

prune213.0ms (1.3%)

regimes204.0ms (1.3%)

regimes69.0ms (0.4%)

regimes60.0ms (0.4%)

regimes53.0ms (0.3%)

regimes74.0ms (0.5%)

regimes62.0ms (0.4%)

regimes45.0ms (0.3%)

regimes50.0ms (0.3%)

regimes38.0ms (0.2%)

regimes32.0ms (0.2%)

regimes16.0ms (0.1%)

regimes15.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0%)

regimes8.0ms (0%)

simplify17.0ms (0.1%)

soundness4.7s (29.3%)

preprocess66.0ms (0.4%)

end0.0ms (0%)

Profiling