Metrics for Beckmann Sample, normalization factor

analyze41.0ms (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: 25.0ms

ival-div: 5.0ms (20% of total)

ival-mult: 3.0ms (12% of total)

ival-sub: 3.0ms (12% of total)

...c/correct-round.rkt:119:19: 3.0ms (12% of total)

ival-sqrt: 3.0ms (12% of total)

ival-add: 2.0ms (8% of total)

ival-exp: 2.0ms (8% of total)

ival-<: 2.0ms (8% of total)

ival-pi: 1.0ms (4% of total)

ival-and: 1.0ms (4% of total)

ival-neg: 1.0ms (4% of total)

const: 0.0ms (0% of total)

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

sample2.0s (15.7%)

Results

1.6s	8256×	0	valid
15.0ms	77×	0	invalid

Precisions

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

ival-div: 213.0ms (17.6% of total)

ival-mult: 159.0ms (13.1% of total)

...c/correct-round.rkt:119:19: 153.0ms (12.6% of total)

ival-sqrt: 150.0ms (12.4% of total)

ival-<: 128.0ms (10.6% of total)

ival-add: 124.0ms (10.2% of total)

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

ival-exp: 66.0ms (5.4% of total)

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

ival-pi: 40.0ms (3.3% of total)

ival-and: 36.0ms (3% of total)

const: 15.0ms (1.2% of total)

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

Bogosity

preprocess193.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	132
1	150	122
2	452	115
3	1608	108
4	5085	108
5	7538	108
0	18	21
1	48	20
2	117	19
3	279	18
4	464	18
5	1029	18
6	2694	18
7	4299	18
8	5809	18
9	7298	18
0	8002	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 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32)))) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (sqrt.f32 (PI.f32)))))

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

explain221.0ms (1.7%)

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

147.0ms

512×

valid

Compiler

Compiled 285 to 56 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-div: 13.0ms (25.9% of total)

ival-mult: 9.0ms (17.9% of total)

ival-add: 7.0ms (14% of total)

ival-sqrt: 7.0ms (14% of total)

ival-sub: 5.0ms (10% of total)

ival-exp: 4.0ms (8% of total)

ival-pi: 2.0ms (4% of total)

ival-neg: 2.0ms (4% of total)

const: 1.0ms (2% 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
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (sqrt.f32 (PI.f32)))))
▶	98.1%	(/.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)))))

Status

Accuracy

Program

▶

98.4%

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

▶

98.1%

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

Compiler

Compiled 51 to 35 computations (31.4% saved)

simplify157.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

1952×	`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	29	209
1	76	209
2	173	190
3	351	190
4	539	190
5	1131	190
6	2910	190
7	4437	190
8	6046	190
9	7464	190
0	8168	190

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize158.0ms (1.2%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
✓	accuracy	99.8%	(sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.9%	(/.f32 (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (sqrt.f32 (PI.f32)))
✓	accuracy	99.6%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.0%	(/.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)))))
✓	accuracy	98.2%	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))

Results

120.0ms

256×

valid

Compiler

Compiled 237 to 30 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-div: 10.0ms (22.9% of total)

ival-mult: 9.0ms (20.6% of total)

ival-pi: 6.0ms (13.8% of total)

ival-sqrt: 6.0ms (13.8% of total)

ival-add: 4.0ms (9.2% of total)

ival-exp: 4.0ms (9.2% of total)

ival-sub: 4.0ms (9.2% of total)

const: 1.0ms (2.3% of total)

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

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

series50.0ms (0.4%)

Counts

12 → 180

Calls

Call 1

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

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

Calls

45 calls:

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

rewrite365.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2656×	`-lowering-.f32`
2656×	`-lowering-.f64`
1364×	`fma-lowering-fma.f32`
1364×	`fma-lowering-fma.f64`
1212×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	149
1	138	143
2	735	126
3	3951	126
0	8485	126

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 867

Calls

Call 1

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

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

simplify484.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

6418×	`-lowering-.f32`
6418×	`-lowering-.f64`
4072×	`+-lowering-+.f64`
4072×	`+-lowering-+.f32`
1334×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	734	7080
1	2383	6250
0	8487	6250

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

eval140.0ms (1.1%)

Compiler: Compiled 32013 to 2862 computations (91.1% saved)

prune176.0ms (1.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	1039	22	1061
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	1041	22	1063

Accuracy

99.8%

Counts

1063 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	92.7%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.8%	(/.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) (sqrt.f32 (PI.f32)))))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (pow.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) #s(literal 1/2 binary32)))) (.f32 (neg.f32 cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))))))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	95.8%	(/.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)))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
▶	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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))))))))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))))))
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.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)))))
	57.4%	(/.f32 #s(literal 1 binary32) (+.f32 (.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 (.f32 cosTheta c) (exp.f32 (*.f32 cosTheta cosTheta)))))) #s(literal 1 binary32)))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	97.6%	(/.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)))
▶	97.6%	(/.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))))))
	57.5%	(/.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
▶	4.8%	(/.f32 #s(literal 1 binary32) c)
	96.4%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (*.f32 cosTheta (PI.f32)))))
	97.6%	(.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))))))))))
	93.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.4%	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))))

Compiler

Compiled 970 to 674 computations (30.5% saved)

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32))))
✓	cost-diff	96	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	96	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	96	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(*.f32 cosTheta #s(literal -2 binary32))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))
✓	cost-diff	0	(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
✓	cost-diff	0	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) c)
✓	cost-diff	96	(/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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)))))
✓	cost-diff	160	(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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))))))
✓	cost-diff	160	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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)))))))
✓	cost-diff	160	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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))))))))

Rules

1592×	`-lowering-.f32`
1592×	`-lowering-.f64`
1406×	`sum3-define`
1076×	`div-sub`
1002×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	409
1	120	377
2	265	368
3	708	363
4	2029	363
5	5046	363
0	8289	363

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize323.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.3%	(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32))))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	accuracy	98.2%	(/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)))
✓	accuracy	97.5%	(pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32))
✓	accuracy	99.8%	(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
✓	accuracy	99.0%	(/.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))))))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))
✓	accuracy	99.9%	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32))))
✓	accuracy	99.9%	(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.9%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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))))))))
✓	accuracy	98.9%	(/.f32 (neg.f32 (/.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 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)))))
✓	accuracy	97.0%	(/.f32 (exp.f32 (*.f32 cosTheta cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
✓	accuracy	96.9%	(pow.f32 (PI.f32) #s(literal -1/2 binary32))

Results

243.0ms

256×

valid

Compiler

Compiled 457 to 50 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-mult: 48.0ms (36.9% of total)

ival-div: 31.0ms (23.8% of total)

ival-pow: 22.0ms (16.9% of total)

ival-add: 10.0ms (7.7% of total)

ival-sqrt: 7.0ms (5.4% of total)

ival-exp: 5.0ms (3.8% of total)

ival-sub: 2.0ms (1.5% of total)

ival-neg: 2.0ms (1.5% of total)

ival-pi: 1.0ms (0.8% of total)

const: 1.0ms (0.8% of total)

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

series51.0ms (0.4%)

Counts

25 → 348

Calls

Call 1

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

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

Calls

87 calls:

Time	Variable		Point	Expression
9.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (/ (sqrt (/ (+ 1 (* cosTheta -2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
8.0ms	cosTheta	@	inf	(/ (neg (/ (exp (* cosTheta cosTheta)) (pow (PI) -1/2))) (/ -1 (* cosTheta (pow (- 1 (* cosTheta 2)) -1/2))))
3.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (/ (- 1 cosTheta) cosTheta) (sqrt (PI)))))
3.0ms	cosTheta	@	inf	(/ 1 (+ 1 (/ (sqrt (/ (+ 1 (* cosTheta -2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
2.0ms	cosTheta	@	-inf	(/ (neg (/ (exp (* cosTheta cosTheta)) (pow (PI) -1/2))) (/ -1 (* cosTheta (pow (- 1 (* cosTheta 2)) -1/2))))

rewrite317.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3896×	`-lowering-.f32`
3896×	`-lowering-.f64`
2716×	`/-lowering-/.f32`
2716×	`/-lowering-/.f64`
974×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	302
1	248	241
2	1314	225
0	8672	225

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 1462

Calls

Call 1

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

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

simplify565.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

6504×	`-lowering-.f32`
6504×	`-lowering-.f64`
4360×	`+-lowering-+.f64`
4360×	`+-lowering-+.f32`
1726×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1105	11083
1	3757	9998
0	8826	9998

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

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

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

eval254.0ms (2%)

Compiler: Compiled 58655 to 7717 computations (86.8% saved)

prune365.0ms (2.8%)

Pruning

34 alts after pruning (31 fresh and 3 done)

	Pruned	Kept	Total
New	2035	26	2061
Fresh	12	5	17
Picked	2	3	5
Done	0	0	0
Total	2049	34	2083

Accuracy

99.8%

Counts

2083 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	92.7%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.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)) c))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32)))))))
✓	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.8%	(/.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) (sqrt.f32 (PI.f32)))))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	57.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 cosTheta cosTheta)) (sqrt.f32 (PI.f32)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.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)))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)))
▶	57.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))))
	57.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
▶	98.2%	(/.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))))))
	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))))))
	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (+.f32 cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (*.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))))
	95.7%	(/.f32 #s(literal 1 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)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))))
	55.0%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c)))) #s(literal 1 binary32)))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1/2 binary32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
▶	97.6%	(/.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)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
✓	97.6%	(/.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))))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) 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)))))
✓	4.8%	(/.f32 #s(literal 1 binary32) c)
	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)))))))
	97.2%	(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 (neg.f32 cosTheta) (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #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)))))))))
▶	93.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	89.9%	(exp.f32 (.f32 (log1p.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))
	90.4%	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))))

Compiler

Compiled 1298 to 914 computations (29.6% saved)

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta)
✓	cost-diff	0	(/.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)))
✓	cost-diff	0	(+.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))))
✓	cost-diff	0	(/.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)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)
✓	cost-diff	128	(/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))
✓	cost-diff	128	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta)))
✓	cost-diff	128	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))))
✓	cost-diff	0	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	cost-diff	0	(+.f32 (/.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))
✓	cost-diff	0	(+.f32 (+.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)) c)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.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)) c))
✓	cost-diff	-32	(sqrt.f32 (PI.f32))
✓	cost-diff	-32	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(*.f32 cosTheta #s(literal -2 binary32))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))
✓	cost-diff	0	(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
✓	cost-diff	0	(+.f32 #s(literal 1 binary32) c)

Rules

1782×	`-lowering-.f32`
1782×	`-lowering-.f64`
1576×	`fma-define`
1388×	`fma-lowering-fma.f32`
1388×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	312
1	87	299
2	160	293
3	328	285
4	771	285
5	1886	284
6	5434	284
0	8040	284

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize272.0ms (2.1%)

Localize:

Found 19 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	99.0%	(/.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)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))
✓	accuracy	98.4%	(/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta)
✓	accuracy	97.5%	(pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))))
✓	accuracy	98.1%	(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta)))
✓	accuracy	96.9%	(pow.f32 (PI.f32) #s(literal -1/2 binary32))
✓	accuracy	60.2%	(/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 cosTheta (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))
✓	accuracy	100.0%	(+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))
✓	accuracy	99.9%	(+.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))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.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)) c))
✓	accuracy	98.9%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	100.0%	(sqrt.f32 (PI.f32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.0%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
✓	accuracy	99.8%	(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
✓	accuracy	99.0%	(/.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))))))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
✓	accuracy	97.5%	(sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))

Results

188.0ms

256×

valid

Compiler

Compiled 356 to 41 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-div: 20.0ms (29.2% of total)

ival-pow: 16.0ms (23.4% of total)

ival-add: 10.0ms (14.6% of total)

ival-mult: 10.0ms (14.6% of total)

ival-sqrt: 7.0ms (10.2% of total)

ival-exp: 2.0ms (2.9% of total)

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

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

const: 1.0ms (1.5% of total)

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

series31.0ms (0.2%)

Counts

25 → 324

Calls

Call 1

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

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

Calls

81 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (* (pow (PI) -1/2) (* cosTheta (- 1 cosTheta))) (* cosTheta cosTheta))))
1.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (sqrt (/ (+ 1 (* cosTheta -2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
1.0ms	c	@	0	(/ 1 (+ (+ (/ (+ (/ 1 cosTheta) -1) (pow (PI) 1/2)) 1) c))
1.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (/ (sqrt (/ (+ 1 (* cosTheta -2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
0.0ms	c	@	inf	(/ 1 (+ (+ (/ (+ (/ 1 cosTheta) -1) (pow (PI) 1/2)) 1) c))

rewrite294.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3074×	`-lowering-.f32`
3074×	`-lowering-.f64`
2172×	`/-lowering-/.f32`
2172×	`/-lowering-/.f64`
1358×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	211
1	185	198
2	861	197
3	5649	197
0	8197	197

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 1132

Calls

Call 1

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

Outputs
(+.f32 #s(literal 1 binary32) c)
(+.f32 c #s(literal 1 binary32))
(neg.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)))
(neg.f32 (.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))))))
(exp.f32 (log.f32 (/.f32 (+.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)))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 cosTheta #s(literal -2 binary32))))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (.f32 cosTheta #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))
(+.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 cosTheta #s(literal -2 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(+.f32 (.f32 (.f32 cosTheta #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(pow.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (PI.f32))) (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 #s(literal 1 binary32) (exp.f32 (log.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))))
(/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1 binary32))
(/.f32 #s(literal -1 binary32) (/.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 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (neg.f32 (PI.f32)))
(/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.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 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta #s(literal -2 binary32)))) (PI.f32))
(/.f32 (exp.f32 (log.f32 (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))) (exp.f32 (log.f32 (neg.f32 (PI.f32)))))
(/.f32 (neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
(/.f32 (neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(/.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 2 binary32)))) (neg.f32 (PI.f32)))
(/.f32 (.f32 #s(literal 1 binary32) (/.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 #s(literal 1 binary32) (/.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 (.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 2 binary32))) #s(literal 1 binary32)) (neg.f32 (PI.f32)))
(/.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(/.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 cosTheta #s(literal 2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (neg.f32 (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))) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(/.f32 (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(/.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 1/4 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(/.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 1/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(/.f32 (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1/3 binary32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1/3 binary32)))
(/.f32 (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal 1/3 binary32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #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 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)))
(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 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 -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 (neg.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (neg.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(.f32 (/.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))) (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))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(.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 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(.f32 (exp.f32 (log1p.f32 (.f32 cosTheta #s(literal -2 binary32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (/.f32 #s(literal -1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))
(.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32))) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32)))) (/.f32 #s(literal -1 binary32) (PI.f32)))
(neg.f32 (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
(+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))
(+.f32 #s(literal 1 binary32) (neg.f32 (*.f32 cosTheta #s(literal 2 binary32))))
(+.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))
(+.f32 (neg.f32 (*.f32 cosTheta #s(literal 2 binary32))) #s(literal 1 binary32))
(fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))
(fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))
(-.f32 #s(literal 0 binary32) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32)))))
(/.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))) #s(literal -1 binary32))
(.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (+.f32 #s(literal -1 binary32) (.f32 cosTheta #s(literal 2 binary32))))
(/.f32 #s(literal -2 binary32) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 (*.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))
(/.f32 (*.f32 cosTheta #s(literal 2 binary32)) #s(literal -1 binary32))
(*.f32 cosTheta #s(literal -2 binary32))
(*.f32 #s(literal -2 binary32) cosTheta)
(.f32 (.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))
(PI.f32)
(log1p.f32 (expm1.f32 (PI.f32)))
(neg.f32 (neg.f32 (PI.f32)))
(exp.f32 (log.f32 (PI.f32)))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32))) #s(literal 2 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))) #s(literal 3 binary32)))
(exp.f32 (.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal 1/2 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1/3 binary32)))
(+.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal -1 binary32))
(fabs.f32 (PI.f32))
(pow.f32 (PI.f32) #s(literal 1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 1/3 binary32))
(pow.f32 (E.f32) (log.f32 (PI.f32)))
(fma.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (neg.f32 (PI.f32)))
(-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32))
(-.f32 (/.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 (PI.f32) #s(literal 1 binary32))
(/.f32 (neg.f32 (PI.f32)) #s(literal -1 binary32))
(sqrt.f32 (*.f32 (PI.f32) (PI.f32)))
(cbrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))
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(*.f32 (PI.f32) #s(literal 1 binary32))
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(.f32 (.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32))) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(.f32 (.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) #s(literal 1/2 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -1 binary32))) (pow.f32 (PI.f32) #s(literal -1/6 binary32)))

simplify366.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

6784×	`-lowering-.f32`
6784×	`-lowering-.f64`
3686×	`+-lowering-+.f64`
3686×	`+-lowering-+.f32`
1252×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	768	8300
1	2533	7320
0	8850	7320

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 324

Calls

Call 1

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

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

eval213.0ms (1.6%)

Compiler: Compiled 43892 to 6455 computations (85.3% saved)

prune277.0ms (2.1%)

Pruning

39 alts after pruning (35 fresh and 4 done)

	Pruned	Kept	Total
New	1838	20	1858
Fresh	11	15	26
Picked	3	2	5
Done	1	2	3
Total	1853	39	1892

Accuracy

100.0%

Counts

1892 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.4%	(/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))
	54.6%	(/.f32 (/.f32 (*.f32 cosTheta cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)
	54.6%	(/.f32 (/.f32 (*.f32 cosTheta cosTheta) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
	54.7%	(/.f32 (*.f32 cosTheta cosTheta) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
▶	92.7%	(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
▶	54.7%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta cosTheta)))
	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))
▶	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 1 binary32)) c))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta) #s(literal 1 binary32)) c))
	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) c))
	57.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) c))
	53.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 cosTheta (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) #s(literal 1 binary32)) c))
	54.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 cosTheta (.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))) #s(literal 1 binary32)) c))
✓	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.8%	(/.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) (sqrt.f32 (PI.f32)))))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	98.2%	(/.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))))))
▶	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 (+.f32 cosTheta #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))))))
	95.7%	(/.f32 #s(literal 1 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)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))))
	55.2%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) c))) #s(literal 1 binary32)))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1/2 binary32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.6%	(/.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))) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) 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)))))
✓	4.8%	(/.f32 #s(literal 1 binary32) c)
▶	93.1%	(*.f32 cosTheta (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)))
	93.1%	(*.f32 cosTheta (/.f32 cosTheta (/.f32 cosTheta (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)))))))
	97.2%	(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.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)))) (neg.f32 cosTheta)) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
	92.6%	(.f32 cosTheta (.f32 cosTheta (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	93.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	89.9%	(exp.f32 (.f32 (log1p.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))
	90.4%	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))))

Compiler

Compiled 1338 to 952 computations (28.8% saved)

simplify174.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(pow.f32 (PI.f32) #s(literal 1/3 binary32))
✓	cost-diff	0	(pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32))
✓	cost-diff	0	(*.f32 cosTheta (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)))
✓	cost-diff	64	(/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
✓	cost-diff	64	(+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 1 binary32))
✓	cost-diff	64	(+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 1 binary32)) c)
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 1 binary32)) c))
✓	cost-diff	0	(pow.f32 (PI.f32) #s(literal 1/2 binary32))
✓	cost-diff	0	(/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	cost-diff	64	(/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta cosTheta))
✓	cost-diff	192	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta cosTheta)))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(pow.f32 (PI.f32) #s(literal -1/2 binary32))
✓	cost-diff	0	(/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
✓	cost-diff	64	(sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))
✓	cost-diff	64	(/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))
✓	cost-diff	64	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))))
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))

Rules

1746×	`-lowering-.f32`
1746×	`-lowering-.f64`
1336×	`fma-lowering-fma.f32`
1336×	`fma-lowering-fma.f64`
1200×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	228
1	90	211
2	169	209
3	369	199
4	773	199
5	1831	199
6	3201	199
7	6533	199
0	8269	199

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize367.0ms (2.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f32 (PI.f32) #s(literal 1/3 binary32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.0%	(*.f32 cosTheta (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)))
✓	accuracy	96.9%	(pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32))
✓	accuracy	99.8%	(*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 1 binary32)) c))
✓	accuracy	98.2%	(/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta))
✓	accuracy	96.9%	(pow.f32 (PI.f32) #s(literal -1/2 binary32))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta cosTheta)))
✓	accuracy	98.9%	(/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	60.4%	(/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta cosTheta))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
✓	accuracy	98.2%	(/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)
✓	accuracy	96.9%	(pow.f32 (PI.f32) #s(literal -1/2 binary32))
✓	accuracy	99.7%	(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))
✓	accuracy	99.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
✓	accuracy	98.4%	(/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))
✓	accuracy	97.5%	(sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))

Results

179.0ms

256×

valid

Compiler

Compiled 267 to 39 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

ival-add: 36.0ms (35.5% of total)

ival-div: 19.0ms (18.7% of total)

ival-pow: 19.0ms (18.7% of total)

ival-mult: 10.0ms (9.9% of total)

ival-exp: 7.0ms (6.9% of total)

...c/correct-round.rkt:119:19: 5.0ms (4.9% of total)

ival-sqrt: 2.0ms (2% of total)

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

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

const: 1.0ms (1% of total)

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

series10.0ms (0.1%)

Counts

21 → 240

Calls

Call 1

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

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

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	c	@	0	(+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (+ 1 (* cosTheta -2)))) (* cosTheta (exp (* cosTheta cosTheta)))))
0.0ms	cosTheta	@	0	(/ (pow (PI) -1/2) cosTheta)
0.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (+ 1 (* cosTheta -2)))) (* cosTheta (exp (* cosTheta cosTheta))))))
0.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (sqrt (* (/ 1 (PI)) (+ 1 (* cosTheta -2)))) (* cosTheta (exp (* cosTheta cosTheta))))))
0.0ms	cosTheta	@	-inf	(/ (pow (PI) -1/2) cosTheta)

rewrite296.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3304×	`-lowering-.f32`
3304×	`-lowering-.f64`
2292×	`/-lowering-/.f32`
2292×	`/-lowering-/.f64`
1708×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	166
1	193	137
2	977	133
3	6833	133
0	8331	133

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 1230

Calls

Call 1

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

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

simplify392.0ms (3%)

Algorithm

1×	egg-herbie

Rules

5004×	`-lowering-.f32`
5004×	`-lowering-.f64`
2964×	`+-lowering-+.f64`
2964×	`+-lowering-+.f32`
1814×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	574	5160
1	1885	4521
2	7432	4517
0	8014	4517

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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

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

eval242.0ms (1.9%)

Compiler: Compiled 33668 to 5558 computations (83.5% saved)

prune282.0ms (2.2%)

Pruning

51 alts after pruning (44 fresh and 7 done)

	Pruned	Kept	Total
New	1834	18	1852
Fresh	4	26	30
Picked	2	3	5
Done	0	4	4
Total	1840	51	1891

Accuracy

100.0%

Counts

1891 → 51

Alt Table

Click to see full alt table

Status	Accuracy	Program
	93.4%	(/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta))
	54.6%	(/.f32 (/.f32 (*.f32 cosTheta cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)
	54.7%	(/.f32 (*.f32 cosTheta cosTheta) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	92.7%	(/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
	51.0%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)))
	92.4%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) cosTheta)) cosTheta))
	92.8%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) cosTheta))
	54.7%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) (*.f32 cosTheta cosTheta)))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
	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))
	55.1%	(/.f32 #s(literal 1 binary32) (/.f32 cosTheta (.f32 cosTheta (.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	93.3%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))) #s(literal 1 binary32)) c))
✓	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 1 binary32)) c))
	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) cosTheta))) #s(literal 1 binary32)) c))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta) #s(literal 1 binary32)) c))
	95.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)) #s(literal 1 binary32)) c))
	57.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (/.f32 (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) c))
	53.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (.f32 cosTheta (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta))) #s(literal 1 binary32)) c))
✓	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.8%	(/.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) (sqrt.f32 (PI.f32)))))
	97.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
✓	98.2%	(/.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))))))
✓	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))
	95.7%	(/.f32 #s(literal 1 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)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) cosTheta))))))
	55.2%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) c))) #s(literal 1 binary32)))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))) #s(literal -1/2 binary32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.6%	(/.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))) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32)))))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	92.5%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) 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)))))
✓	4.8%	(/.f32 #s(literal 1 binary32) c)
	54.6%	(*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) cosTheta) (/.f32 cosTheta (/.f32 #s(literal 1 binary32) cosTheta)))
	54.6%	(.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) cosTheta) (.f32 cosTheta cosTheta))
	50.6%	(.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	55.1%	(.f32 (/.f32 #s(literal 1 binary32) cosTheta) (.f32 cosTheta (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	93.1%	(*.f32 cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 3/2 binary32)))
	92.7%	(*.f32 cosTheta (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)))
	93.1%	(*.f32 cosTheta (/.f32 cosTheta (/.f32 cosTheta (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)))))))
	97.2%	(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.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)))) (neg.f32 cosTheta)) (*.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
	92.8%	(.f32 cosTheta (.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) cosTheta) cosTheta))
	93.1%	(.f32 cosTheta (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	93.3%	(.f32 cosTheta (.f32 (*.f32 cosTheta (/.f32 #s(literal -1 binary32) cosTheta)) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
	92.6%	(.f32 cosTheta (.f32 cosTheta (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
✓	93.5%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	89.9%	(exp.f32 (.f32 (log1p.f32 (/.f32 (pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))
	90.4%	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (/.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta)))))))

Compiler

Compiled 2324 to 1016 computations (56.3% saved)

regimes227.0ms (1.8%)

Counts

88 → 1

Calls

Call 1

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

Calls

6 calls:

80.0ms	(+.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))))
35.0ms	(.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)))
29.0ms	(+.f32 #s(literal 1 binary32) c)
26.0ms	c
24.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.5%	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)

regimes202.0ms (1.6%)

Counts

81 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

47.0ms	(+.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))))
40.0ms	(+.f32 #s(literal 1 binary32) c)
31.0ms	(/.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
22.0ms	(.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
98.4%	1	`cosTheta`
98.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.4%	1	`(+.f32 #s(literal 1 binary32) c)`
98.4%	1	`c`
98.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes70.0ms (0.5%)

Counts

79 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

23.0ms	cosTheta
22.0ms	c
18.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta`
98.2%	1	`c`
98.2%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes66.0ms (0.5%)

Counts

72 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

20.0ms	c
20.0ms	cosTheta
18.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta`
98.2%	1	`c`
98.2%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes84.0ms (0.7%)

Counts

69 → 1

Calls

Call 1

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

Outputs

(/.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) (sqrt.f32 (PI.f32)))))

Calls

3 calls:

43.0ms	cosTheta
18.0ms	c
18.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes84.0ms (0.6%)

Counts

56 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

42.0ms	(+.f32 #s(literal 1 binary32) c)
23.0ms	cosTheta
15.0ms	c

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes58.0ms (0.4%)

Counts

54 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

17.0ms	c
14.0ms	cosTheta
12.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes40.0ms (0.3%)

Counts

43 → 1

Calls

Call 1

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

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

Calls

3 calls:

13.0ms	c
11.0ms	cosTheta
9.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
96.2%	1	`cosTheta`
96.2%	1	`c`
96.2%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes32.0ms (0.2%)

Counts

36 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	cosTheta
10.0ms	c
8.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
96.2%	1	`(+.f32 #s(literal 1 binary32) c)`
96.2%	1	`cosTheta`
96.2%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes28.0ms (0.2%)

Counts

31 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	c
9.0ms	cosTheta
8.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes44.0ms (0.3%)

Counts

23 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	c
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
93.5%	1	`cosTheta`
93.5%	1	`c`

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

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

Calls

2 calls:

1.0ms	c
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
4.8%	1	`cosTheta`
4.8%	1	`c`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

68×	`+-commutative_binary32`
46×	`*-commutative_binary32`
30×	`sub-neg_binary32`
26×	`neg-sub0_binary32`
26×	`neg-mul-1_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	204
1	132	204
2	155	203
3	179	203
4	201	203
5	213	203
6	217	203
7	218	203

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.5s (19.7%)

Rules

6504×	`-lowering-.f32`
6504×	`-lowering-.f64`
6418×	`-lowering-.f32`
6418×	`-lowering-.f64`
4360×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	48	20
2	117	19
3	279	18
4	464	18
5	1029	18
6	2694	18
7	4299	18
8	5809	18
9	7298	18
0	8002	18
0	734	7080
1	2383	6250
0	8487	6250
0	40	211
1	185	198
2	861	197
3	5649	197
0	8197	197
0	49	302
1	248	241
2	1314	225
0	8672	225
0	1105	11083
1	3757	9998
0	8826	9998
0	29	149
1	138	143
2	735	126
3	3951	126
0	8485	126

Stop Event

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

Compiler

Compiled 427 to 249 computations (41.7% saved)

preprocess64.0ms (0.5%)

Compiler: Compiled 464 to 202 computations (56.5% saved)

analyze41.0ms (0.3%)

sample2.0s (15.7%)

preprocess193.0ms (1.5%)

explain221.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify157.0ms (1.2%)

localize158.0ms (1.2%)

series50.0ms (0.4%)

rewrite365.0ms (2.8%)

simplify484.0ms (3.7%)

eval140.0ms (1.1%)

prune176.0ms (1.4%)

simplify127.0ms (1%)

localize323.0ms (2.5%)

series51.0ms (0.4%)

rewrite317.0ms (2.4%)

simplify565.0ms (4.4%)

eval254.0ms (2%)

prune365.0ms (2.8%)

simplify142.0ms (1.1%)

localize272.0ms (2.1%)

series31.0ms (0.2%)

rewrite294.0ms (2.3%)

simplify366.0ms (2.8%)

eval213.0ms (1.6%)

prune277.0ms (2.1%)

simplify174.0ms (1.3%)

localize367.0ms (2.8%)

series10.0ms (0.1%)

rewrite296.0ms (2.3%)

simplify392.0ms (3%)

eval242.0ms (1.9%)

prune282.0ms (2.2%)

regimes227.0ms (1.8%)

regimes202.0ms (1.6%)

regimes70.0ms (0.5%)

regimes66.0ms (0.5%)

regimes84.0ms (0.7%)

regimes84.0ms (0.6%)

regimes58.0ms (0.4%)

regimes40.0ms (0.3%)

regimes32.0ms (0.2%)

regimes28.0ms (0.2%)

regimes44.0ms (0.3%)

regimes3.0ms (0%)

simplify16.0ms (0.1%)

soundness2.5s (19.7%)

preprocess64.0ms (0.5%)

end0.0ms (0%)

Profiling