Metrics for Beckmann Sample, normalization factor

analyze47.0ms (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: 23.0ms

ival-div: 4.0ms (17.1% of total)

ival-mult: 3.0ms (12.8% of total)

...c/correct-round.rkt:119:19: 3.0ms (12.8% of total)

ival-sqrt: 3.0ms (12.8% of total)

ival-add: 2.0ms (8.5% of total)

ival-exp: 2.0ms (8.5% of total)

ival-sub: 2.0ms (8.5% of total)

ival-<: 2.0ms (8.5% of total)

ival-pi: 1.0ms (4.3% of total)

ival-and: 1.0ms (4.3% of total)

ival-neg: 1.0ms (4.3% of total)

const: 0.0ms (0% of total)

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

sample2.1s (14.6%)

Results

1.5s	8256×	0	valid
10.0ms	61×	0	invalid

Precisions

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

ival-div: 205.0ms (16.8% of total)

ival-mult: 178.0ms (14.6% of total)

ival-sqrt: 163.0ms (13.3% of total)

...c/correct-round.rkt:119:19: 152.0ms (12.4% of total)

ival-<: 120.0ms (9.8% of total)

ival-add: 117.0ms (9.6% of total)

ival-sub: 83.0ms (6.8% of total)

ival-exp: 63.0ms (5.2% of total)

ival-pi: 46.0ms (3.8% of total)

ival-neg: 41.0ms (3.4% of total)

ival-and: 36.0ms (2.9% of total)

const: 15.0ms (1.2% of total)

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

Bogosity

preprocess203.0ms (1.4%)

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	150	122
2	453	115
3	1613	108
4	5093	108
5	7568	108
0	18	21
1	48	20
2	117	19
3	279	18
4	464	18
5	1029	18
6	2691	18
7	4299	18
8	5812	18
9	7301	18
0	8005	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 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta 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) (/ (rsqrt (PI)) (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 (+ 1 (fnmadd (/ (sqrt (sum3 1 cosTheta cosTheta)) cosTheta) (/ (rsqrt (PI)) (exp (square cosTheta))) c)))
(/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
(recip (fma (/ (sqrt (fma cosTheta -2 1)) cosTheta) (/ (rsqrt (PI)) (exp (square 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 (fmsub (/ (sqrt (sum3 1 cosTheta cosTheta)) cosTheta) (/ (rsqrt (PI)) (exp (square cosTheta))) (+ 1 c)))
(neg (/ 1 (+ (+ 1 (neg c)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))))
(recip (+ -1 (fnmadd (/ (sqrt (fma cosTheta -2 1)) cosTheta) (/ (rsqrt (PI)) (exp (square cosTheta))) c)))
(/ 1 (+ (+ 1 cosTheta) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 c) c)) c)) (exp (* (neg c) c)))))
(recip (fma (/ (sqrt (fma c -2 1)) c) (/ (rsqrt (PI)) (exp (square c))) (+ 1 cosTheta)))

explain207.0ms (1.4%)

FPErrors

Click to see full error table

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

Results

125.0ms

512×

valid

Compiler

Compiled 285 to 56 computations (80.4% saved)

Precisions

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

ival-div: 21.0ms (34.7% of total)

ival-mult: 11.0ms (18.2% of total)

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

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

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

ival-exp: 5.0ms (8.3% of total)

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

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

const: 1.0ms (1.7% 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
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))

Status

Accuracy

Program

▶

97.9%

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

▶

98.5%

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

Compiler

Compiled 51 to 35 computations (31.4% saved)

simplify158.0ms (1.1%)

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	32	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	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	0	(/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
✓	cost-diff	0	(+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta 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	217
1	78	213
2	180	199
3	351	199
4	527	199
5	1121	199
6	2895	199
7	4422	199
8	6021	199
9	7439	199
0	8143	199

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize199.0ms (1.4%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.0%	(*.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%	(sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
✓	accuracy	99.2%	(/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))
✓	accuracy	98.8%	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))

Results

155.0ms

256×

valid

Compiler

Compiled 248 to 31 computations (87.5% saved)

Precisions

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

ival-div: 32.0ms (47.7% of total)

ival-mult: 11.0ms (16.4% of total)

ival-exp: 7.0ms (10.4% of total)

ival-sqrt: 6.0ms (9% of total)

ival-add: 5.0ms (7.5% of total)

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

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

const: 1.0ms (1.5% of total)

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

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

series66.0ms (0.5%)

Counts

12 → 180

Calls

Call 1

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

Calls

45 calls:

Time	Variable		Point	Expression
14.0ms	cosTheta	@	inf	(* (sqrt (PI)) (* cosTheta (exp (* cosTheta cosTheta))))
10.0ms	cosTheta	@	inf	(/ 1 (+ c (+ 1 (/ (sqrt (- 1 (* cosTheta 2))) (* (sqrt (PI)) (* cosTheta (exp (* cosTheta cosTheta))))))))
6.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))))
5.0ms	cosTheta	@	-inf	(/ 1 (+ c (+ 1 (/ (sqrt (- 1 (* cosTheta 2))) (* (sqrt (PI)) (* cosTheta (exp (* cosTheta cosTheta))))))))
3.0ms	cosTheta	@	inf	(* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))

rewrite518.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

5992×	`-lowering-.f32`
5992×	`-lowering-.f64`
2976×	`/-lowering-/.f32`
2976×	`/-lowering-/.f64`
2802×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	158
1	208	148
2	1904	138
0	10019	138

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 689

Calls

Call 1

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

Outputs
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(sqrt.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
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(.f32 (neg.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #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))))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) #s(literal -8 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32)))))))
(.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 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))))
(.f32 (.f32 (+.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))))

simplify372.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6516×	`-lowering-.f32`
6516×	`-lowering-.f64`
4180×	`+-lowering-+.f64`
4180×	`+-lowering-+.f32`
1316×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	729	7281
1	2383	6422
0	8571	6422

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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

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

eval153.0ms (1.1%)

Compiler: Compiled 38806 to 4473 computations (88.5% saved)

prune183.0ms (1.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	844	25	869
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	846	25	871

Accuracy

99.9%

Counts

871 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.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))))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	98.0%	(/.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))) (/.f32 (-.f32 #s(literal 1 binary32) c) (-.f32 #s(literal 1 binary32) (.f32 c c)))) cosTheta) (.f32 cosTheta (/.f32 (-.f32 #s(literal 1 binary32) c) (-.f32 #s(literal 1 binary32) (.f32 c c))))))
	98.0%	(/.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))) (-.f32 c #s(literal 1 binary32))) (.f32 cosTheta (-.f32 (.f32 c c) #s(literal 1 binary32)))) (.f32 cosTheta (-.f32 c #s(literal 1 binary32)))))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
▶	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	98.3%	(/.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 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	95.6%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (+.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.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)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))))
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.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)) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))
	97.8%	(/.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)))
	97.8%	(/.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))))))
	98.0%	(/.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)))
	54.8%	(/.f32 #s(literal 1 binary32) (.f32 c (+.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)))))
▶	5.0%	(/.f32 #s(literal 1 binary32) c)
	56.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (/.f32 (.f32 (exp.f32 (neg.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))) cosTheta) #s(literal 2 binary32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (exp.f32 (neg.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))) cosTheta)))
	56.1%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.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 2 binary32)))) (-.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))))))
	96.1%	(.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)))))
	97.2%	(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (neg.f32 (+.f32 (.f32 cosTheta (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.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 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))))
	93.6%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1266 to 804 computations (36.5% saved)

simplify196.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2416×	`fma-define`
2150×	`sum4-define`
1702×	`fma-lowering-fma.f32`
1702×	`fma-lowering-fma.f64`
1232×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	409
1	117	381
2	245	380
3	494	372
4	1094	371
5	2222	371
6	4244	371
7	6827	371
0	8140	371

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize363.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) cosTheta)
✓	accuracy	99.2%	(/.f32 #s(literal 1 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)))
✓	accuracy	99.2%	(/.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 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) cosTheta))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.6%	(/.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))
✓	accuracy	99.9%	(sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
✓	accuracy	99.2%	(/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32)))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32))))))))
✓	accuracy	98.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.6%	(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
✓	accuracy	98.1%	(/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.9%	(pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32))
✓	accuracy	99.8%	(/.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))))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.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)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	accuracy	98.8%	(/.f32 (/.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.f32 (PI.f32) #s(literal 1/2 binary32)))

Results

284.0ms

256×

valid

Compiler

Compiled 479 to 49 computations (89.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-div: 21.0ms (25% of total)

ival-pow: 16.0ms (19% of total)

ival-mult: 15.0ms (17.8% of total)

ival-add: 11.0ms (13.1% of total)

ival-exp: 9.0ms (10.7% of total)

ival-sqrt: 6.0ms (7.1% of total)

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

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

const: 1.0ms (1.2% of total)

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

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

series97.0ms (0.7%)

Counts

25 → 384

Calls

Call 1

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

Calls

96 calls:

Time	Variable		Point	Expression
25.0ms	c	@	-inf	(/ 1 (+ (+ 1 c) (* (/ 1 (/ (pow (PI) 1/2) (/ (pow (+ 1 (* cosTheta -2)) 1/2) cosTheta))) (exp (* (neg cosTheta) cosTheta)))))
24.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (* (- 1 cosTheta) (sqrt (/ 1 (PI)))) cosTheta)))
3.0ms	c	@	0	(/ 1 (+ c (+ 1 (/ (sqrt (- 1 (* cosTheta 2))) (* (+ (* cosTheta cosTheta) 1) (* cosTheta (sqrt (PI))))))))
2.0ms	cosTheta	@	-inf	(/ 1 (+ c (+ 1 (/ (sqrt (- 1 (* cosTheta 2))) (* (+ (* cosTheta cosTheta) 1) (* cosTheta (sqrt (PI))))))))
2.0ms	cosTheta	@	inf	(/ 1 (+ c (+ 1 (/ (sqrt (- 1 (* cosTheta 2))) (* (+ (* cosTheta cosTheta) 1) (* cosTheta (sqrt (PI))))))))

rewrite354.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3050×	`fma-lowering-fma.f32`
3050×	`fma-lowering-fma.f64`
2300×	`-lowering-.f32`
2300×	`-lowering-.f64`
2126×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	308
1	342	276
2	3397	266
0	8340	266

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 738

Calls

Call 1

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

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

simplify516.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

5456×	`-lowering-.f32`
5456×	`-lowering-.f64`
3632×	`+-lowering-+.f64`
3632×	`+-lowering-+.f32`
1986×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1259	12633
1	4203	11413
0	8831	11413

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

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

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)))))))
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(+ (* 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)))))))
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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)
(/.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 #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 cosTheta (exp.f32 (.f32 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 (.f32 cosTheta c) (exp.f32 (.f32 cosTheta cosTheta))))))) 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 (.f32 cosTheta c) (exp.f32 (.f32 cosTheta cosTheta))))) (/.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 (.f32 cosTheta c) (exp.f32 (.f32 cosTheta cosTheta)))) (+.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 (neg.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)))))) 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)))))))))))
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c
(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (exp (pow cosTheta 2))))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (exp (pow cosTheta 2)))) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
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(+ 1 (+ 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))))) (+ (* -1/16 (* (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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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (/.f32 (pow.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)))) #s(literal 2 binary32)) (.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 (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
(/.f32 (-.f32 (-.f32 #s(literal 1 binary32) (/.f32 (pow.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)))) #s(literal 3 binary32)) (.f32 c (.f32 c c)))) (-.f32 (+.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))) (/.f32 (pow.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)))) #s(literal 2 binary32)) (.f32 c c)))) c)
(/ 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 (/ (- (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2) c) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (pow.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)))) #s(literal 2 binary32)) 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 (/ (- (/ (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 3) c) (pow (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) 2)) c)) (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 (/.f32 (pow.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)))) #s(literal 3 binary32)) c) (pow.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)))) #s(literal 2 binary32))) (neg.f32 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))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.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)))))))))))
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(/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI)))))
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(- (+ (* -1 (* (/ 1 (* (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 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (sqrt (/ 1 (PI))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))
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(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))) cosTheta)) (/ 1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
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(+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI)))))
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(+ 1 (+ c (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))))
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(+ 1 (+ c (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))))
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(+ 1 (+ c (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))))
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c
(* c (+ 1 (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ (- 1 cosTheta) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) c)) 1)))
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(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))))) c)) 1)))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.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)))))))
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(+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
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(+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
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(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
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(+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
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(+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
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1
#s(literal 1 binary32)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
c
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
c
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* c (+ 1 (/ 1 c)))
(+.f32 #s(literal 1 binary32) c)
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/.f32 (-.f32 (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 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
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(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(/ 1 (+ 1 (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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(/ 1 (+ 1 c))
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(+ 1 (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
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(+ 1 (+ c (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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(+ 1 (+ c (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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(+ 1 (+ c (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
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c
(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (+ 1 (pow cosTheta 2))))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (+ 1 (pow cosTheta 2))))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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(* c (+ 1 (+ (* (/ 1 (* c (* cosTheta (+ 1 (pow cosTheta 2))))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
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c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.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 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.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 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ 1 (* cosTheta (+ 1 (pow cosTheta 2)))) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(.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 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.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 (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.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))))))))))) cosTheta)
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
(+ 1 (+ c (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))))
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(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))))))
(+.f32 #s(literal 1 binary32) (+.f32 (-.f32 c (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))))) (+.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32)))))))
(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (* (sqrt (/ 1 (* (pow cosTheta 13) (PI)))) (sqrt -2)))))))))
(+.f32 #s(literal 1 binary32) (+.f32 (-.f32 c (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))))) (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 11 binary32))))) (sqrt.f32 #s(literal -2 binary32)))) (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 13 binary32))) (PI.f32))))))))))
(+ 1 c)
(+.f32 #s(literal 1 binary32) c)
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2))))))
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(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))))))
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(+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 6)))))))
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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 (+ (* -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 #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))) #s(literal -3/2 binary32)))))) 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)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (+.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 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)))))))))) cosTheta)
1
#s(literal 1 binary32)
(+ 1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)))
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(+ 1 (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)))))
(+.f32 (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))))) (+.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32))))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2)) (* (sqrt (/ 1 (* (pow cosTheta 13) (PI)))) (sqrt -2))))))))
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1
#s(literal 1 binary32)
(+ 1 (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2)))))
(-.f32 #s(literal 1 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)) (sqrt.f32 #s(literal 2 binary32)))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4)))))
(-.f32 (-.f32 #s(literal 1 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)) (sqrt.f32 #s(literal 2 binary32))))) (/.f32 (-.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32))))
(+ 1 (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 4))) (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 6))))))
(+.f32 #s(literal 1 binary32) (-.f32 (-.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32)))) (/.f32 (-.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))) (+.f32 (.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) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))))) (pow.f32 cosTheta #s(literal 6 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 (+ (* -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 (* (pow cosTheta 5) (PI)))) (sqrt -2))
(.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))))
(/ (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))))) (*.f32 cosTheta cosTheta))
(/ (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (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)) (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32)))) (+.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 #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 #s(literal -2 binary32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32)))))))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))))) (*.f32 cosTheta cosTheta))
(/ (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (sqrt -2))) (+ (* -1 (* (sqrt (/ 1 (* (pow cosTheta 13) (PI)))) (sqrt -2))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (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)))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 11) (PI)))) (/ 1 (sqrt -2)))) (+ (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)) (* (sqrt (/ 1 (* (pow cosTheta 9) (PI)))) (sqrt -2))))))))))) (pow cosTheta 2))
(/.f32 (+.f32 (neg.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 13 binary32))) (PI.f32)))))) (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (sqrt.f32 #s(literal -2 binary32)))) (+.f32 (+.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 #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))))) (+.f32 (+.f32 (.f32 #s(literal 1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (.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 (.f32 (sqrt.f32 #s(literal -2 binary32)) (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 9 binary32))))))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 11 binary32))))) (sqrt.f32 #s(literal -2 binary32))))))))) (.f32 cosTheta cosTheta))
(* -1 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))
(/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (/.f32 (-.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))
(/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (neg.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (/.f32 (-.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))) (+.f32 (.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) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (.f32 cosTheta cosTheta))
(/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))) (pow cosTheta 2))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2))))))) (pow cosTheta 6))) (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))) (pow cosTheta 4)))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (neg.f32 (+.f32 (/.f32 (-.f32 (+.f32 (.f32 #s(literal 1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))) (+.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 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))))) (pow.f32 cosTheta #s(literal 6 binary32))) (/.f32 (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32)))) (+.f32 (.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) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))))) (pow.f32 cosTheta #s(literal 4 binary32))))) (/.f32 (-.f32 (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))))) (.f32 cosTheta cosTheta))
(* (/ 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)
(/.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 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 #s(literal -2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (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 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))))) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 #s(literal -2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (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)))) (+ (* 1/16 (* (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 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 (sqrt.f32 #s(literal -2 binary32)) #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 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))))) (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 #s(literal -2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (-.f32 #s(literal 0 binary32) (*.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)) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (PI.f32))))))
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c
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c
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(.f32 cosTheta (+.f32 (+.f32 (.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 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.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))))))
(* cosTheta (+ (* -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 cosTheta (+.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 #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 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.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 cosTheta) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 cosTheta)))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 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))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 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))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 #s(literal -1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (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) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.f32 #s(literal -1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (+.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))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 #s(literal 1/16 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))))))))
(* 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 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (+.f32 (.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 (PI.f32) cosTheta))) (.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)))))))
(* 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 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (+.f32 (.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 (PI.f32) cosTheta))) (.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 #s(literal -1/2 binary32) (.f32 (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 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (/.f32 (+.f32 (.f32 (PI.f32) #s(literal 1/16 binary32)) (.f32 #s(literal -1/64 binary32) (/.f32 (.f32 cosTheta (PI.f32)) #s(literal 1/2 binary32)))) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 #s(literal -1/16 binary32) (/.f32 (.f32 (sqrt.f32 (.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32))))) (.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 #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 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -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))))
(+.f32 (+.f32 (.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 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.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)))))
(+ (* -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 #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 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (*.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 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (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))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (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)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (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))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 #s(literal 1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))))
(+ (* -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)))))))
(+.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))) (sqrt.f32 #s(literal 2 binary32)))) (.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (+.f32 (.f32 #s(literal 1/8 binary32) (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (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)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))))))

eval192.0ms (1.3%)

Compiler: Compiled 42025 to 4190 computations (90% saved)

prune156.0ms (1.1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	1158	18	1176
Fresh	10	10	20
Picked	4	1	5
Done	0	0	0
Total	1172	29	1201

Accuracy

99.9%

Counts

1201 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.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))))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (-.f32 #s(literal 1 binary32) c)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 cosTheta (-.f32 #s(literal 1 binary32) c))))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal 1 binary32)) c))
▶	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	97.5%	(/.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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	98.0%	(/.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))))))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) cosTheta)))))
	93.1%	(/.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 #s(literal 1 binary32) cosTheta))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	52.6%	(/.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)))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (/.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))))))
▶	97.4%	(/.f32 #s(literal 1 binary32) (+.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)))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	10.7%	(/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32)))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	97.8%	(/.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)))
	97.4%	(/.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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
▶	97.8%	(/.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))))))
▶	95.5%	(/.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)))))
✓	5.0%	(/.f32 #s(literal 1 binary32) c)
	95.5%	(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (/.f32 c (pow.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)))) #s(literal 2 binary32))))
	53.7%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
	55.7%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 c c) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))))) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))))))
	96.1%	(.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)))))
	93.6%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Compiler

Compiled 1241 to 814 computations (34.4% saved)

simplify206.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

2022×	`sum5-define`
1614×	`-lowering-.f32`
1614×	`-lowering-.f64`
1484×	`fnmsub-define`
1408×	`sum4-define`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	47	357
1	107	334
2	204	334
3	301	333
4	531	330
5	1031	330
6	1989	320
7	4831	319
0	8175	319

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize284.0ms (2%)

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	99.2%	(/.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))))))
✓	accuracy	98.1%	(/.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	99.2%	(/.f32 #s(literal 1 binary32) (+.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)))) 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	99.9%	(+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))
✓	accuracy	99.2%	(/.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)))))
✓	accuracy	98.0%	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	100.0%	(+.f32 c #s(literal 1 binary32))
✓	accuracy	99.8%	(/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32)))
✓	accuracy	99.9%	(/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32))))
✓	accuracy	99.8%	(.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	accuracy	98.8%	(/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))

Results

201.0ms

256×

valid

Compiler

Compiled 407 to 48 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-div: 42.0ms (41.1% of total)

ival-mult: 18.0ms (17.6% of total)

ival-add: 15.0ms (14.7% of total)

ival-pow: 15.0ms (14.7% of total)

ival-exp: 4.0ms (3.9% of total)

ival-sqrt: 4.0ms (3.9% of total)

ival-pi: 1.0ms (1% of total)

const: 1.0ms (1% of total)

ival-neg: 1.0ms (1% of total)

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

series74.0ms (0.5%)

Counts

23 → 312

Calls

Call 1

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

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

78 calls:

Time	Variable		Point	Expression
25.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (/ (sqrt (/ (+ 1 (* cosTheta -2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
8.0ms	cosTheta	@	inf	(/ 1 (+ 1 (/ (sqrt (/ (+ 1 (* cosTheta -2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
5.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (/ (exp (neg (* cosTheta cosTheta))) (* cosTheta (pow (+ 1 (* cosTheta -2)) -1/2))) (pow (PI) 1/2))))
3.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (/ (exp (neg (* cosTheta cosTheta))) (* cosTheta (pow (+ 1 (* cosTheta -2)) -1/2))) (pow (PI) 1/2))))
2.0ms	cosTheta	@	-inf	(/ 1 (+ c (+ 1 (/ (/ (+ 1 (* cosTheta (+ (* cosTheta -3/2) -1))) cosTheta) (pow (PI) 1/2)))))

rewrite389.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3412×	`-lowering-.f32`
3412×	`-lowering-.f64`
2306×	`fma-lowering-fma.f32`
2306×	`fma-lowering-fma.f64`
1746×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	264
1	341	240
2	3530	240
0	8927	240

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 692

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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))))))))
(exp.f32 (.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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)))
(pow.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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))
(pow.f32 (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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)))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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)))))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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))))))))
(.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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))))))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 (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))
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(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta #s(literal -3/2 binary32)) (.f32 (.f32 cosTheta cosTheta) #s(literal 9/4 binary32)))) cosTheta) (+.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 9/4 binary32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 3/2 binary32)))))
(/.f32 (.f32 (+.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 9/4 binary32)) #s(literal -1 binary32)) cosTheta) (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal 1 binary32)))
(.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal -3/2 binary32)))))
(.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))
(.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))) cosTheta)
(.f32 (.f32 cosTheta (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal -3/2 binary32)))) #s(literal 1 binary32))
(.f32 (.f32 #s(literal 1 binary32) cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal -3/2 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal -3/2 binary32)))) cosTheta)
(neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (neg.f32 (PI.f32))))
(neg.f32 (/.f32 (-.f32 #s(literal 0 binary32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) (PI.f32)))
(exp.f32 (.f32 (log.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) #s(literal 1 binary32)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) #s(literal 1 binary32)))
(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(/.f32 (-.f32 #s(literal 0 binary32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) (neg.f32 (PI.f32)))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (-.f32 (.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32))) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32)))) #s(literal 1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (-.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)))) (PI.f32)))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32)))) #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (-.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)))) (neg.f32 (PI.f32))))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32))) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32))) #s(literal -1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (-.f32 #s(literal 0 binary32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))) (neg.f32 (neg.f32 (PI.f32))))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1 binary32)) (PI.f32))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal -1 binary32)) (neg.f32 (PI.f32)))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (-.f32 (.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)))))
(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1 binary32)) (PI.f32))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1 binary32)))
(.f32 (-.f32 #s(literal 0 binary32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))))
(.f32 (.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (-.f32 (.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))))))
(.f32 (pow.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 4 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))

simplify371.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

6208×	`-lowering-.f32`
6208×	`-lowering-.f64`
4476×	`+-lowering-+.f64`
4476×	`+-lowering-+.f32`
1512×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1064	8983
1	3647	8167
0	8736	8167

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

Inputs
(/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)))) c)
(/ 1 c)
(* -1 (/ (- (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (neg (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))
(+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (+ c (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
c
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (exp (neg (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+ 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)))))))
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c
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(/ 1 (+ 1 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 2)))))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))))))
(- (/ 1 (+ 1 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 2)))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 2)))))) (* 1/4 (/ 1 (* (pow cosTheta 3) (* (PI) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 3))))))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (sqrt -1) (- (* -1/4 (/ cosTheta (* (PI) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 3)))))) (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 2)))))))) (* (exp (pow cosTheta 2)) (* (sqrt 2) (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))))))))) (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (* (pow (sqrt 2) 5) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 3)))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 2)))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (* (pow (sqrt 2) 3) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 2)))))) (* 1/4 (/ 1 (* (pow cosTheta 3) (* (PI) (* (pow (exp (pow cosTheta 2)) 2) (* (pow (sqrt 2) 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))) 3))))))))))
(* (/ 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)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))
(+ 1 (+ (* 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 (+ (* -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 (+ (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))))
(+ 1 (+ (* -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 (+ (* -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 (+ (* -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))))))))
cosTheta
(* cosTheta (+ 1 cosTheta))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* 3/2 cosTheta)))))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* cosTheta (+ 3/2 (* 5/2 cosTheta)))))))
(* (sqrt cosTheta) (sqrt -1/2))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2)))))
(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (+ 1/16 (* 1/64 (/ cosTheta (pow (sqrt -1/2) 2)))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))))
(* (sqrt cosTheta) (* (sqrt -1) (sqrt 1/2)))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (+ 1/16 (* -1/64 (/ cosTheta (pow (sqrt 1/2) 2))))) (sqrt 1/2)))) (* -1/16 (* (sqrt cosTheta) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(/ 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)) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -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))))
(/ 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 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(/.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)))
(+ (* -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)))))))
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(+ (* 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)))))))
(+.f32 (/.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 c (+.f32 (/.f32 c (pow.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)) #s(literal 3 binary32))) (/.f32 #s(literal -1 binary32) (pow.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)) #s(literal 2 binary32))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
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(/ 1 c)
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(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (neg (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
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(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) c))) c)
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(/ 1 c)
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(* -1 (/ (- (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
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(* -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))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -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 (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 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2/3 binary32)) (.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)))
(+ 1 (+ c (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 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) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)))
(+ 1 (+ c (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 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) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)))
(+ 1 (+ c (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 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) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)))
c
(* c (+ 1 (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
(+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (*.f32 cosTheta c))))) #s(literal 1 binary32))
(* c (+ 1 (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
(+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (*.f32 cosTheta c))))) #s(literal 1 binary32))
(* c (+ 1 (+ (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
(+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) (*.f32 cosTheta c))))) #s(literal 1 binary32))
c
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 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) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta))) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 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) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta))) (neg.f32 c)) #s(literal -1 binary32)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta) (sqrt (/ 1 (PI))))) 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) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta))) (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 (+ (* -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 #s(literal 1 binary32) (+.f32 c (-.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 (+ 1 (+ c (+ (* -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 #s(literal 1 binary32) (+.f32 c (-.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))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(.f32 cosTheta (+.f32 (-.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)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 c cosTheta))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (-.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)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 c cosTheta)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (-.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)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 c 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 (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (*.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 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)))
(* (/ 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 (+ (* -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 #s(literal 1 binary32) (.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 (+ 1 (+ (* -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 #s(literal 1 binary32) (.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))))) (/ 1 cosTheta))))
(+.f32 (.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))) #s(literal 1 binary32))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)))))
(.f32 cosTheta (+.f32 (-.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)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)))))
(.f32 cosTheta (+.f32 (-.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)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta 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 (+ (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
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(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
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(/ (+ (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)
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(+ 1 (* (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 (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)
(/.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 #s(literal 1 binary32) (.f32 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))))) (+ (* 1/16 (* (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)))))))
(+.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 (.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) (.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)))))) (+.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 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (exp.f32 (*.f32 cosTheta cosTheta)))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2)))))
(/.f32 (.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)))) (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 #s(literal 1 binary32) (.f32 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)))))))
(+.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 cosTheta cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (/.f32 (.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)))) (exp.f32 (.f32 cosTheta cosTheta)))) (.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 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))))
(+ (* -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))))))))
(+.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 cosTheta cosTheta))) (sqrt.f32 #s(literal 2 binary32)))) (/.f32 (.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)))) (exp.f32 (.f32 cosTheta cosTheta)))) (+.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 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (exp.f32 (.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 cosTheta cosTheta))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32)))))))
(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))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+.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))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(+.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))))))
(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(*.f32 (sqrt.f32 #s(literal -2 binary32)) (sqrt.f32 (/.f32 cosTheta (PI.f32))))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(.f32 cosTheta (+.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)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(.f32 cosTheta (+.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 -1/8 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))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(.f32 cosTheta (+.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 #s(literal 1 binary32) (*.f32 (PI.f32) (pow.f32 cosTheta #s(literal 7 binary32))))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(neg.f32 (.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(neg.f32 (.f32 cosTheta (+.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 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(.f32 (neg.f32 cosTheta) (+.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 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))) (PI.f32))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(.f32 (neg.f32 cosTheta) (+.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 -1 binary32)) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))) (+.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 1/16 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))))))))
cosTheta
(* cosTheta (+ 1 cosTheta))
(*.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* 3/2 cosTheta)))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 3/2 binary32))))))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* cosTheta (+ 3/2 (* 5/2 cosTheta)))))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal 3/2 binary32) (.f32 cosTheta #s(literal 5/2 binary32))))))))
(* (sqrt cosTheta) (sqrt -1/2))
(*.f32 (sqrt.f32 cosTheta) (sqrt.f32 #s(literal -1/2 binary32)))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))
(.f32 cosTheta (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (*.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2)))))
(.f32 cosTheta (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (+.f32 (.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal -1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -1/2 binary32)))))))
(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (+ 1/16 (* 1/64 (/ cosTheta (pow (sqrt -1/2) 2)))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))))
(.f32 cosTheta (+.f32 (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (sqrt.f32 #s(literal -1/2 binary32)))) (+.f32 (.f32 (sqrt.f32 #s(literal -1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal -1/16 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -1/2 binary32)))))) (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (+.f32 #s(literal 1/16 binary32) (*.f32 #s(literal 1/64 binary32) (/.f32 cosTheta #s(literal -1/2 binary32))))) (sqrt.f32 #s(literal -1/2 binary32))))))
(* (sqrt cosTheta) (* (sqrt -1) (sqrt 1/2)))
(.f32 (sqrt.f32 cosTheta) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(.f32 (neg.f32 cosTheta) (-.f32 (+.f32 (.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 #s(literal 1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (+ 1/16 (* -1/64 (/ cosTheta (pow (sqrt 1/2) 2))))) (sqrt 1/2)))) (* -1/16 (* (sqrt cosTheta) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(.f32 (neg.f32 cosTheta) (-.f32 (-.f32 (.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (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 #s(literal 1 binary32) cosTheta))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (/.f32 (+.f32 #s(literal 1/16 binary32) (.f32 #s(literal -1/64 binary32) (/.f32 cosTheta #s(literal 1/2 binary32)))) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 #s(literal -1/16 binary32) (/.f32 (.f32 (sqrt.f32 cosTheta) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) 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) 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 (- (* 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)) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))
(.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))
(+.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal 1/2 binary32) (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+.f32 (+.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal 1/2 binary32) (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))))) (.f32 #s(literal -1/8 binary32) (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (exp (neg (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (exp (neg (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(+.f32 (.f32 #s(literal -1/8 binary32) (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (+.f32 (+.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))) (.f32 #s(literal 1/2 binary32) (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))))) (.f32 #s(literal 1/16 binary32) (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))))))))
(* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(-.f32 (.f32 #s(literal -1/2 binary32) (.f32 (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+.f32 (-.f32 (.f32 #s(literal -1/2 binary32) (.f32 (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (.f32 #s(literal 1/8 binary32) (.f32 (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(+.f32 (-.f32 (.f32 #s(literal -1/2 binary32) (.f32 (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (.f32 (.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)))) (+.f32 (.f32 #s(literal 1/8 binary32) (.f32 (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32))) (.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))) (.f32 #s(literal -1/16 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (*.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -1 binary32)))) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))))))
(* (/ 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)))))))
(.f32 (neg.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)))))))
(.f32 (neg.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)
(neg.f32 cosTheta)
(* cosTheta (- (* -3/2 cosTheta) 1))
(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))
(* cosTheta (- (* -3/2 cosTheta) 1))
(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))
(* cosTheta (- (* -3/2 cosTheta) 1))
(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))
(* -3/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal -3/2 binary32))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -3/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal -3/2 binary32))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(* -1 (* (pow cosTheta 2) (+ 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))))
(/ 1 (PI))
(/.f32 #s(literal 1 binary32) (PI.f32))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32))))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32))))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32))))
(* -2 (/ cosTheta (PI)))
(*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))
(* -2 (/ cosTheta (PI)))
(*.f32 #s(literal -2 binary32) (/.f32 cosTheta (PI.f32)))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(neg.f32 (.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))))))
(neg.f32 (.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))))))
(neg.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 2 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32))))))

eval123.0ms (0.9%)

Compiler: Compiled 32757 to 3920 computations (88% saved)

prune155.0ms (1.1%)

Pruning

40 alts after pruning (38 fresh and 2 done)

	Pruned	Kept	Total
New	983	21	1004
Fresh	6	17	23
Picked	3	2	5
Done	1	0	1
Total	993	40	1033

Accuracy

99.9%

Counts

1033 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(pow.f32 (pow.f32 (+.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))))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	53.6%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) #s(literal 1 binary32)) (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal 1 binary32))))
	10.7%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) (-.f32 #s(literal 1 binary32) c)))
	95.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (-.f32 #s(literal 1 binary32) c)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 cosTheta (-.f32 #s(literal 1 binary32) c))))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal 1 binary32)))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal 1 binary32)) c))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) 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)))))
▶	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	97.5%	(/.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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	98.0%	(/.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))))))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) cosTheta)))))
	52.6%	(/.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)))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta))))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (sqrt.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
✓	10.7%	(/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32)))
	97.8%	(/.f32 #s(literal 1 binary32) (+.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)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta)))
▶	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
▶	53.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1 binary32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	53.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.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)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	97.8%	(/.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)))
	97.4%	(/.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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
✓	97.8%	(/.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))))))
	92.8%	(/.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 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
	95.5%	(/.f32 #s(literal 1 binary32) (+.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)))))
	96.8%	(/.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) (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta))))
	95.5%	(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (/.f32 c (pow.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)))) #s(literal 2 binary32))))
	10.7%	(-.f32 #s(literal 1 binary32) c)
	53.7%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (pow.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal 2 binary32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
	55.0%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 c c) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32)))))))) #s(literal 2 binary32)))) (-.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))))))))
	53.5%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))) (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
▶	96.1%	(.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)))))))
	93.6%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
▶	10.7%	#s(literal 1 binary32)

Compiler

Compiled 1614 to 1068 computations (33.8% saved)

simplify504.0ms (3.5%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

2058×	`fnmadd-define`
1814×	`sum4-define`
1442×	`sum3-define`
1358×	`-lowering-.f32`
1358×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	279
1	98	270
2	209	265
3	527	259
4	1480	259
5	3829	259
0	8028	259

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize254.0ms (1.8%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.1%	(*.f32 cosTheta (PI.f32))
✓	accuracy	98.8%	(.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)))))))
✓	accuracy	96.9%	(-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1 binary32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))))
✓	accuracy	99.0%	(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1 binary32)))
✓	accuracy	96.9%	(pow.f32 (PI.f32) #s(literal -1/2 binary32))
✓	accuracy	56.2%	(/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1 binary32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	100.0%	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	accuracy	99.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	accuracy	98.7%	(/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	99.9%	(/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32))))
✓	accuracy	99.8%	(.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
✓	accuracy	98.8%	(/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))

Results

158.0ms

256×

valid

Compiler

Compiled 330 to 42 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-pow: 19.0ms (27.2% of total)

ival-div: 17.0ms (24.3% of total)

ival-mult: 12.0ms (17.2% of total)

ival-add: 9.0ms (12.9% of total)

ival-exp: 4.0ms (5.7% of total)

ival-sqrt: 4.0ms (5.7% of total)

ival-sub: 2.0ms (2.9% 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)

series35.0ms (0.2%)

Counts

21 → 228

Calls

Call 1

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

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

57 calls:

Time	Variable		Point	Expression
14.0ms	cosTheta	@	inf	(* cosTheta (- (sqrt (PI)) (* (* cosTheta (PI)) (- 1 (sqrt (/ 1 (PI)))))))
3.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (/ (/ (exp (neg (* cosTheta cosTheta))) (* cosTheta (pow (+ 1 (* cosTheta -2)) -1/2))) (pow (PI) 1/2))))
3.0ms	cosTheta	@	inf	(/ 1 (+ 1 (/ (/ (exp (neg (* cosTheta cosTheta))) (* cosTheta (pow (+ 1 (* cosTheta -2)) -1/2))) (pow (PI) 1/2))))
1.0ms	cosTheta	@	0	(* cosTheta (- (sqrt (PI)) (* (* cosTheta (PI)) (- 1 (sqrt (/ 1 (PI)))))))
1.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (/ 1 cosTheta) (pow (PI) 1/2))))

rewrite315.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3030×	`-lowering-.f32`
3030×	`-lowering-.f64`
2342×	`fma-lowering-fma.f32`
2342×	`fma-lowering-fma.f64`
1734×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	210
1	295	170
2	2776	168
0	8235	168

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 589

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))))))
(exp.f32 (.f32 (log1p.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))
(pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))
(pow.f32 (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))))))
(.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))
(.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (neg.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))))))))
(.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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 -1/2 binary32)) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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 -1/2 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (pow.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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 3 binary32)))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) 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 2 binary32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (pow.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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 3 binary32)))) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) 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 2 binary32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) 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 2 binary32))))) (-.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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))))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (pow.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) 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 2 binary32))))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))
(+.f32 #s(literal 1 binary32) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 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)))))
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(*.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (pow.f32 (PI.f32) #s(literal -1/3 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (PI.f32)) #s(literal -1/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 1 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) #s(literal 2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/12 binary32)) #s(literal 2 binary32)))
(.f32 (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/4 binary32))) #s(literal -1/2 binary32)) (pow.f32 (PI.f32) #s(literal -1/8 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal -1 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32))) #s(literal -1 binary32)))
(*.f32 (pow.f32 #s(literal -1 binary32) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/8 binary32)))
(.f32 (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))
(.f32 (pow.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/12 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -1/8 binary32)) #s(literal 2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/8 binary32)) #s(literal 2 binary32)))
(exp.f32 (*.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32))))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32))) #s(literal -1 binary32)))
(exp.f32 (*.f32 (-.f32 #s(literal 0 binary32) (log.f32 (PI.f32))) #s(literal 1/2 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (PI.f32))) #s(literal -1/4 binary32)))
(exp.f32 (*.f32 (log.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32))) #s(literal 2 binary32)))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/4 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal -2 binary32))
(pow.f32 (*.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/4 binary32))
(pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1 binary32)) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
(/.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (neg.f32 (PI.f32))))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(*.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1 binary32)) #s(literal -1/2 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal -1/8 binary32)) (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/8 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal -1/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (pow.f32 (PI.f32) #s(literal -1/3 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (PI.f32)) #s(literal -1/4 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 1 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -1/6 binary32)) #s(literal 2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/12 binary32)) #s(literal 2 binary32)))
(.f32 (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/4 binary32))) #s(literal -1/2 binary32)) (pow.f32 (PI.f32) #s(literal -1/8 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal -1 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal -1 binary32)) (pow.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32))) #s(literal -1 binary32)))
(*.f32 (pow.f32 #s(literal -1 binary32) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/8 binary32)))
(.f32 (pow.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))
(.f32 (pow.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/12 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal -1/8 binary32)) #s(literal 2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal -1/8 binary32)) #s(literal 2 binary32)))
(+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 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))) #s(literal 1 binary32))
(pow.f32 (/.f32 (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -3/2 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal -1 binary32))
(fma.f32 #s(literal -1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal -1 binary32)) #s(literal 1 binary32))
(fma.f32 (*.f32 #s(literal -1 binary32) (pow.f32 (PI.f32) #s(literal -1/4 binary32))) (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (/.f32 (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -3/2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -3/2 binary32))) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -3/2 binary32)))) (neg.f32 (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))) (neg.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (pow.f32 (PI.f32) #s(literal -3/2 binary32)))) (+.f32 #s(literal 1 binary32) (-.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 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))))
(/.f32 (-.f32 #s(literal 1 binary32) (*.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 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))
(*.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -3/2 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))))
(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (+.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 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.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 (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))

simplify323.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

6104×	`-lowering-.f32`
6104×	`-lowering-.f64`
2498×	`+-lowering-+.f64`
2498×	`+-lowering-+.f32`
1944×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	609	4896
1	2064	4339
2	7948	4335
0	8030	4335

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))))))
(/ 1 (+ 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) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 1 (* -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 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 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) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))))
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(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
cosTheta
(* cosTheta (+ 1 cosTheta))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* 3/2 cosTheta)))))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* cosTheta (+ 3/2 (* 5/2 cosTheta)))))))
(* (sqrt cosTheta) (sqrt -1/2))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2)))))
(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (+ 1/16 (* 1/64 (/ cosTheta (pow (sqrt -1/2) 2)))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))))
(* (sqrt cosTheta) (* (sqrt -1) (sqrt 1/2)))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (+ 1/16 (* -1/64 (/ cosTheta (pow (sqrt 1/2) 2))))) (sqrt 1/2)))) (* -1/16 (* (sqrt cosTheta) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(* 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 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (neg.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))) (.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 (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (.f32 (-.f32 (-.f32 (.f32 (.f32 (PI.f32) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))) (.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)))) (sqrt.f32 (PI.f32))))) (neg.f32 cosTheta)) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))) (.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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta cosTheta))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (neg (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2))))))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 2 binary32))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (neg (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))))
(+.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))) (/.f32 (+.f32 (/.f32 (.f32 (.f32 #s(literal -1/4 binary32) cosTheta) (exp.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 3 binary32)) (.f32 (PI.f32) #s(literal -2 binary32)))) (/.f32 (.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 2 binary32)))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta)))))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 2 binary32))))
(- (+ (* -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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (sqrt -2)))) 2))))))))
(-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta)))))) (/.f32 (+.f32 (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (+.f32 (/.f32 (.f32 (.f32 #s(literal -1/4 binary32) cosTheta) (exp.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 3 binary32)) (.f32 (PI.f32) #s(literal -2 binary32)))) (/.f32 (.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32)))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32)))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 2 binary32)))) (+.f32 (sqrt.f32 #s(literal -2 binary32)) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) #s(literal -2 binary32))))) (.f32 #s(literal 1/16 binary32) (+.f32 (/.f32 (.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 2 binary32))) (/.f32 (/.f32 (.f32 (.f32 cosTheta cosTheta) (exp.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (.f32 (PI.f32) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 4 binary32)))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 3 binary32)))))) (pow.f32 cosTheta #s(literal 6 binary32)))) (+.f32 (/.f32 (.f32 #s(literal -1/4 binary32) (exp.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))) (.f32 (.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal -2 binary32))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 3 binary32)))) (+.f32 (/.f32 (.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal -2 binary32))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal 2 binary32))) (/.f32 (/.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)))))) (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal -2 binary32))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (/.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (*.f32 cosTheta cosTheta))))) #s(literal 2 binary32))))))
(/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 1 binary32)) (exp.f32 (*.f32 cosTheta cosTheta)))))))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (neg (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (neg (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
(+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 1 binary32)) (exp.f32 (.f32 cosTheta cosTheta))))))) (/.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32)) (.f32 (sqrt.f32 #s(literal -1 binary32)) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 #s(literal 2 binary32))))) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal 2 binary32)) (/.f32 (.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 1 binary32)) (exp.f32 (*.f32 cosTheta cosTheta)))))) #s(literal 2 binary32))))
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(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))
(* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))) (pow cosTheta 2))
(/.f32 (.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta cosTheta))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))) (pow cosTheta 2))
(/.f32 (.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta cosTheta))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))) (pow cosTheta 2))
(/.f32 (.f32 (+.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta cosTheta))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* -1 (sqrt (/ 1 (PI))))
(neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))
(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(* -1 (* (pow cosTheta 2) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 cosTheta) (sqrt (PI)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 cosTheta) (sqrt (PI)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 cosTheta) (sqrt (PI)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* -1 (* (pow cosTheta 2) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 cosTheta) (sqrt (PI)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 cosTheta) (sqrt (PI)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))) (* (/ 1 cosTheta) (sqrt (PI)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(sqrt (PI))
(sqrt.f32 (PI.f32))
(+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))))
(-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))))
(-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))))
(-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 (.f32 cosTheta (PI.f32))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* cosTheta (- (* (/ 1 cosTheta) (sqrt (PI))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (- (* (/ 1 cosTheta) (sqrt (PI))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (- (* (/ 1 cosTheta) (sqrt (PI))) (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))
(.f32 (neg.f32 (.f32 cosTheta (PI.f32))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))
(* -1 (* cosTheta (- (* -1 (* (/ 1 cosTheta) (sqrt (PI)))) (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 0 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(* -1 (* cosTheta (- (* -1 (* (/ 1 cosTheta) (sqrt (PI)))) (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 0 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(* -1 (* cosTheta (- (* -1 (* (/ 1 cosTheta) (sqrt (PI)))) (* -1 (* (PI) (- 1 (sqrt (/ 1 (PI)))))))))
(.f32 (neg.f32 cosTheta) (+.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 #s(literal 0 binary32) (/.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
(* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))
(.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))
cosTheta
(* cosTheta (+ 1 cosTheta))
(*.f32 cosTheta (+.f32 cosTheta #s(literal 1 binary32)))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* 3/2 cosTheta)))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 3/2 binary32))))))
(* cosTheta (+ 1 (* cosTheta (+ 1 (* cosTheta (+ 3/2 (* 5/2 cosTheta)))))))
(.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal 3/2 binary32) (.f32 cosTheta #s(literal 5/2 binary32))))))))
(* (sqrt cosTheta) (sqrt -1/2))
(*.f32 (sqrt.f32 cosTheta) (sqrt.f32 #s(literal -1/2 binary32)))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))
(.f32 cosTheta (+.f32 (/.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1/2 binary32))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -1/2 binary32)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2)))))
(.f32 cosTheta (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -1/2 binary32))) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1/2 binary32))) (+.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (*.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32)))))))))
(* cosTheta (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (+ 1/16 (* 1/64 (/ cosTheta (pow (sqrt -1/2) 2)))) (sqrt -1/2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -1/2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (sqrt -1/2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -1/2))))))
(.f32 cosTheta (+.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1/2 binary32))) (+.f32 (.f32 #s(literal -1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 #s(literal -1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))))) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 #s(literal -1/2 binary32))) (/.f32 (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32)))) (+.f32 #s(literal 1/16 binary32) (/.f32 (.f32 cosTheta #s(literal 1/64 binary32)) #s(literal -1/2 binary32)))) #s(literal -1/2 binary32)) (sqrt.f32 #s(literal -1/2 binary32))))))
(* (sqrt cosTheta) (* (sqrt -1) (sqrt 1/2)))
(.f32 (sqrt.f32 #s(literal -1 binary32)) (.f32 (sqrt.f32 #s(literal 1/2 binary32)) (sqrt.f32 cosTheta)))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2)))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))) (.f32 (sqrt.f32 #s(literal 1/2 binary32)) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (sqrt 1/2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(.f32 (neg.f32 cosTheta) (-.f32 (.f32 (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))) (+.f32 (.f32 #s(literal 1/8 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 #s(literal 1/16 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 5 binary32))))))) (.f32 (sqrt.f32 #s(literal 1/2 binary32)) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))))
(* -1 (* cosTheta (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 1/2)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 cosTheta)) (/ (* (sqrt -1) (+ 1/16 (* -1/64 (/ cosTheta (pow (sqrt 1/2) 2))))) (sqrt 1/2)))) (* -1/16 (* (sqrt cosTheta) (/ (sqrt -1) (sqrt 1/2))))) (pow cosTheta 3))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 1/2))))))))
(.f32 (neg.f32 cosTheta) (-.f32 (-.f32 (.f32 #s(literal 1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32))))) (/.f32 (+.f32 (.f32 #s(literal -1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta)) (.f32 (+.f32 #s(literal 1/16 binary32) (/.f32 (.f32 cosTheta #s(literal -1/64 binary32)) #s(literal 1/2 binary32))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 1/2 binary32)))))) (/.f32 (.f32 (.f32 #s(literal -1/16 binary32) (sqrt.f32 cosTheta)) (sqrt.f32 #s(literal -1 binary32))) (sqrt.f32 #s(literal 1/2 binary32)))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (.f32 (sqrt.f32 #s(literal 1/2 binary32)) (*.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) cosTheta))))))
(* 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))

eval119.0ms (0.8%)

Compiler: Compiled 28258 to 4115 computations (85.4% saved)

prune190.0ms (1.3%)

Pruning

47 alts after pruning (43 fresh and 4 done)

	Pruned	Kept	Total
New	1071	21	1092
Fresh	11	22	33
Picked	3	2	5
Done	0	2	2
Total	1085	47	1132

Accuracy

100.0%

Counts

1132 → 47

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.1%	(fma.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) cosTheta (.f32 (neg.f32 (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))) cosTheta))
	96.4%	(/.f32 (.f32 (-.f32 (PI.f32) (pow.f32 (.f32 (.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) #s(literal 2 binary32))) cosTheta) (+.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
	50.7%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)) (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c))) (-.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))))
	10.7%	(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) (-.f32 #s(literal 1 binary32) c)))
	95.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (-.f32 #s(literal 1 binary32) c)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 c c)))) (.f32 cosTheta (-.f32 #s(literal 1 binary32) c))))
	95.5%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
	92.9%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	50.7%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) (-.f32 (*.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)) #s(literal 1 binary32)) c))
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) 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)))))
	97.5%	(/.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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	98.0%	(/.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))))))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (-.f32 #s(literal 1 binary32) cosTheta)))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) #s(literal 1 binary32)))
	50.0%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)))) #s(literal 1 binary32)))
	93.5%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta))))
✓	10.7%	(/.f32 #s(literal 1 binary32) (+.f32 c #s(literal 1 binary32)))
	97.8%	(/.f32 #s(literal 1 binary32) (+.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)) (exp.f32 (.f32 cosTheta cosTheta))) cosTheta)))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	97.9%	(/.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 (+.f32 #s(literal -3/2 binary32) (*.f32 cosTheta #s(literal 1/2 binary32))))))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	97.4%	(/.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))))) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	53.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))))
✓	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal -1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	93.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	53.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.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)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	97.8%	(/.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)))
	97.4%	(/.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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
✓	97.8%	(/.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))))))
	92.8%	(/.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 (sqrt.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (/.f32 #s(literal -2 binary32) (PI.f32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
	95.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
	53.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) #s(literal -1 binary32)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))))
	95.5%	(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))) (/.f32 c (pow.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)))) #s(literal 2 binary32))))
	10.7%	(-.f32 #s(literal 1 binary32) c)
	50.6%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 (+.f32 #s(literal 1 binary32) c) (+.f32 #s(literal 1 binary32) c)) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)))
	55.0%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (.f32 c c) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32)))))))) #s(literal 2 binary32)))) (-.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal -3/2 binary32))))))))))
	53.5%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))) (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	58.7%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
	96.0%	(.f32 cosTheta (-.f32 (sqrt.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3 binary32))) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
	96.1%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (*.f32 cosTheta (PI.f32)))))
	93.3%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	93.6%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	10.7%	#s(literal 1 binary32)

Compiler

Compiled 2733 to 1059 computations (61.3% saved)

regimes275.0ms (1.9%)

Counts

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

Outputs

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

Calls

6 calls:

132.0ms	(+.f32 #s(literal 1 binary32) c)
36.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
27.0ms	cosTheta
25.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
24.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
98.5%	1	`cosTheta`
98.5%	1	`c`
98.5%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.5%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.5%	1	`(+.f32 #s(literal 1 binary32) c)`
98.5%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes63.0ms (0.4%)

Counts

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

Outputs

(/.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))))))

Calls

3 calls:

19.0ms	c
18.0ms	cosTheta
16.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
98.0%	1	`cosTheta`
98.0%	1	`c`
98.0%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes55.0ms (0.4%)

Counts

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

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

Results

Accuracy	Segments	Branch
98.0%	1	`cosTheta`
98.0%	1	`c`
98.0%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes64.0ms (0.4%)

Counts

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

Calls

3 calls:

25.0ms	cosTheta
22.0ms	c
12.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
98.0%	1	`cosTheta`
98.0%	1	`c`
98.0%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes50.0ms (0.3%)

Counts

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

Outputs

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

Calls

3 calls:

24.0ms	(+.f32 #s(literal 1 binary32) c)
11.0ms	c
11.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.9%	1	`(+.f32 #s(literal 1 binary32) c)`
97.9%	1	`cosTheta`
97.9%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes116.0ms (0.8%)

Counts

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

Outputs

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

Calls

3 calls:

93.0ms	cosTheta
11.0ms	c
9.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
97.5%	1	`c`
97.5%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes36.0ms (0.3%)

Counts

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

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 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))

Calls

3 calls:

11.0ms	c
10.0ms	cosTheta
8.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.4%	1	`c`
97.4%	1	`(+.f32 #s(literal 1 binary32) c)`
97.4%	1	`cosTheta`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes30.0ms (0.2%)

Counts

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

Outputs

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

Calls

3 calls:

10.0ms	cosTheta
9.0ms	c
7.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.4%	1	`cosTheta`
97.4%	1	`c`
97.4%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes29.0ms (0.2%)

Counts

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

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

Calls

3 calls:

10.0ms	c
8.0ms	cosTheta
7.0ms	(+.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)

regimes21.0ms (0.1%)

Counts

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

Calls

3 calls:

9.0ms	cosTheta
6.0ms	c
5.0ms	(+.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)

regimes17.0ms (0.1%)

Counts

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

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

Calls

3 calls:

5.0ms	cosTheta
5.0ms	c
4.0ms	(+.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)

regimes13.0ms (0.1%)

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
93.6%	1	`cosTheta`
93.6%	1	`(+.f32 #s(literal 1 binary32) c)`
93.6%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes347.0ms (2.4%)

Counts

5 → 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 c #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 c c)) (-.f32 #s(literal 1 binary32) c)))

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

Calls

2 calls:

344.0ms	c
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
10.7%	1	`c`
10.7%	1	`cosTheta`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (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:

1.0ms	cosTheta
1.0ms	c

Results

Accuracy	Segments	Branch
10.7%	1	`cosTheta`
10.7%	1	`c`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

60×	`+-commutative_binary32`
34×	`*-commutative_binary32`
14×	`sub-neg_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	219
1	130	219
2	144	219
3	152	219
4	157	219
5	158	219

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness3.7s (25.7%)

Rules

6516×	`-lowering-.f32`
6516×	`-lowering-.f64`
6208×	`-lowering-.f32`
6208×	`-lowering-.f64`
6104×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	609	4896
1	2064	4339
2	7948	4335
0	8030	4335
0	1259	12633
1	4203	11413
0	8831	11413
0	729	7281
1	2383	6422
0	8571	6422
0	48	308
1	342	276
2	3397	266
0	8340	266
0	30	158
1	208	148
2	1904	138
0	10019	138
0	18	21
1	48	20
2	117	19
3	279	18
4	464	18
5	1029	18
6	2691	18
7	4299	18
8	5812	18
9	7301	18
0	8005	18
0	47	264
1	341	240
2	3530	240
0	8927	240
0	1064	8983
1	3647	8167
0	8736	8167

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 638 to 394 computations (38.2% saved)

preprocess58.0ms (0.4%)

Compiler: Compiled 496 to 202 computations (59.3% saved)

analyze47.0ms (0.3%)

sample2.1s (14.6%)

preprocess203.0ms (1.4%)

explain207.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify158.0ms (1.1%)

localize199.0ms (1.4%)

series66.0ms (0.5%)

rewrite518.0ms (3.6%)

simplify372.0ms (2.6%)

eval153.0ms (1.1%)

prune183.0ms (1.3%)

simplify196.0ms (1.4%)

localize363.0ms (2.5%)

series97.0ms (0.7%)

rewrite354.0ms (2.5%)

simplify516.0ms (3.6%)

eval192.0ms (1.3%)

prune156.0ms (1.1%)

simplify206.0ms (1.4%)

localize284.0ms (2%)

series74.0ms (0.5%)

rewrite389.0ms (2.7%)

simplify371.0ms (2.6%)

eval123.0ms (0.9%)

prune155.0ms (1.1%)

simplify504.0ms (3.5%)

localize254.0ms (1.8%)

series35.0ms (0.2%)

rewrite315.0ms (2.2%)

simplify323.0ms (2.3%)

eval119.0ms (0.8%)

prune190.0ms (1.3%)

regimes275.0ms (1.9%)

regimes63.0ms (0.4%)

regimes55.0ms (0.4%)

regimes64.0ms (0.4%)

regimes50.0ms (0.3%)

regimes116.0ms (0.8%)

regimes36.0ms (0.3%)

regimes30.0ms (0.2%)

regimes29.0ms (0.2%)

regimes21.0ms (0.1%)

regimes17.0ms (0.1%)

regimes13.0ms (0.1%)

regimes347.0ms (2.4%)

regimes3.0ms (0%)

simplify13.0ms (0.1%)

soundness3.7s (25.7%)

preprocess58.0ms (0.4%)

end0.0ms (0%)

Profiling