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 (20.4% of total)

ival-mult: 3.0ms (12.2% of total)

...c/correct-round.rkt:119:19: 3.0ms (12.2% of total)

ival-sqrt: 3.0ms (12.2% of total)

ival-add: 2.0ms (8.1% of total)

ival-exp: 2.0ms (8.1% of total)

ival-sub: 2.0ms (8.1% of total)

ival-<: 2.0ms (8.1% of total)

ival-pi: 1.0ms (4.1% of total)

ival-and: 1.0ms (4.1% of total)

ival-neg: 1.0ms (4.1% of total)

const: 0.0ms (0% of total)

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

sample2.5s (17.7%)

Results

2.1s	8256×	0	valid
10.0ms	61×	0	invalid

Precisions

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

ival-mult: 338.0ms (22.6% of total)

ival-div: 207.0ms (13.9% of total)

ival-add: 195.0ms (13% of total)

ival-sqrt: 166.0ms (11.1% of total)

...c/correct-round.rkt:119:19: 146.0ms (9.8% of total)

ival-<: 138.0ms (9.2% of total)

ival-sub: 88.0ms (5.9% of total)

ival-exp: 71.0ms (4.8% of total)

ival-pi: 47.0ms (3.1% of total)

ival-neg: 45.0ms (3% of total)

ival-and: 35.0ms (2.3% of total)

const: 14.0ms (0.9% of total)

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

Bogosity

preprocess266.0ms (1.9%)

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)))

explain242.0ms (1.7%)

FPErrors

Click to see full error table

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

Results

148.0ms

512×

valid

Compiler

Compiled 285 to 56 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-pi: 17.0ms (21.4% of total)

ival-mult: 12.0ms (15.1% of total)

ival-sub: 12.0ms (15.1% of total)

ival-div: 11.0ms (13.9% of total)

ival-add: 9.0ms (11.4% of total)

ival-sqrt: 8.0ms (10.1% of total)

ival-exp: 7.0ms (8.8% of total)

ival-neg: 2.0ms (2.5% of total)

const: 1.0ms (1.3% 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
▶	98.2%	(/.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)))))
▶	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

98.2%

(/.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)))))

▶

97.6%

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

Compiler

Compiled 51 to 35 computations (31.4% saved)

simplify186.0ms (1.3%)

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

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)

localize344.0ms (2.5%)

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	99.9%	(sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
✓	accuracy	99.1%	(/.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	98.5%	(/.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	99.7%	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
✓	accuracy	99.1%	(/.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)))))
✓	accuracy	98.0%	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
✓	accuracy	96.9%	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))

Results

158.0ms

256×

valid

Compiler

Compiled 237 to 30 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-neg: 33.0ms (45.5% of total)

ival-div: 11.0ms (15.2% of total)

ival-mult: 9.0ms (12.4% of total)

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

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

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

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

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

const: 1.0ms (1.4% of total)

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

series127.0ms (0.9%)

Counts

12 → 180

Calls

Call 1

Inputs
#<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) (* (* (/ 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 (+ (+ 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
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#<alt (* cosTheta (sqrt (PI)))>
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#<alt (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))>
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#<alt (* 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)))))))))>
#<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
39.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (/ (sqrt (- 1 (* cosTheta 2))) (* cosTheta (exp (* cosTheta cosTheta)))) (sqrt (PI)))))
5.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (/ (sqrt (- 1 (* cosTheta 2))) (* cosTheta (exp (* cosTheta cosTheta)))) (sqrt (PI)))))
4.0ms	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)))))
3.0ms	cosTheta	@	inf	(+ (+ 1 c) (/ (/ (sqrt (- 1 (* cosTheta 2))) (* cosTheta (exp (* cosTheta cosTheta)))) (sqrt (PI))))

rewrite617.0ms (4.4%)

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	734	126
3	3953	126
0	8500	126

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 867

Calls

Call 1

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

simplify387.0ms (2.8%)

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	8491	6250

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

eval103.0ms (0.7%)

Compiler: Compiled 32059 to 2871 computations (91% saved)

prune188.0ms (1.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1041	20	1061
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	1043	20	1063

Accuracy

99.8%

Counts

1063 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.9%	(/.f32 #s(literal 1 binary32) (/.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))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (/.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)))
	96.0%	(/.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)))))
▶	97.4%	(/.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)))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
▶	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (/.f32 cosTheta (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32))))))
	97.7%	(/.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)))))
	61.2%	(/.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)))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (exp.f32 (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))) cosTheta)))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
▶	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	61.2%	(/.f32 #s(literal 1 binary32) (.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
▶	5.2%	(/.f32 #s(literal 1 binary32) c)
	96.5%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
	93.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.8%	(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 790 to 560 computations (29.1% saved)

simplify159.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

1748×	`sum3-define`
1686×	`sum4-define`
1410×	`+-lowering-+.f64`
1410×	`+-lowering-+.f32`
1368×	`--lowering--.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	45	360
1	111	337
2	238	334
3	377	333
4	653	333
5	1294	333
6	3320	325
0	8030	325

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize264.0ms (1.9%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
✓	accuracy	98.3%	(/.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	98.2%	(PI.f32)
✓	accuracy	97.6%	(sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -2 binary32))) (PI.f32)))
✓	accuracy	99.4%	(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))
✓	accuracy	99.1%	(/.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)))))
✓	accuracy	98.4%	(/.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)))
✓	accuracy	98.2%	(PI.f32)
✓	accuracy	99.9%	(+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.4%	(/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))
✓	accuracy	98.2%	(PI.f32)
✓	accuracy	100.0%	(/.f32 #s(literal 1 binary32) c)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (/.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32)) cosTheta) (exp.f32 (.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) c)))
✓	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	98.2%	(PI.f32)
✓	accuracy	97.6%	(pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32)) #s(literal 1/2 binary32))

Results

176.0ms	251×	0	valid
17.0ms	5×	5	exit

Compiler

Compiled 409 to 46 computations (88.8% saved)

Precisions

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

ival-div: 24.0ms (34.4% of total)

ival-add: 14.0ms (20% of total)

ival-mult: 13.0ms (18.6% of total)

ival-pow: 6.0ms (8.6% of total)

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

backward-pass: 3.0ms (4.3% of total)

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

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

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

const: 1.0ms (1.4% of total)

series36.0ms (0.3%)

Counts

21 → 348

Calls

Call 1

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

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

87 calls:

Time	Variable		Point	Expression
3.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (/ (/ (+ 1 (* cosTheta (+ (* cosTheta (+ (* cosTheta 1/2) -3/2)) -1))) cosTheta) (sqrt (PI)))))
2.0ms	c	@	inf	(/ 1 (+ (+ 1 c) (/ (/ 1 cosTheta) (sqrt (PI)))))
2.0ms	cosTheta	@	inf	(/ 1 (+ (+ 1 c) (/ (/ (+ 1 (* cosTheta (+ (* cosTheta (+ (* cosTheta 1/2) -3/2)) -1))) cosTheta) (sqrt (PI)))))
1.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (/ (+ 1 (* cosTheta (+ (* cosTheta (+ (* cosTheta 1/2) -3/2)) -1))) cosTheta) (sqrt (PI)))))
1.0ms	cosTheta	@	-inf	(/ 1 (+ (+ 1 c) (/ (/ (+ 1 (* cosTheta (+ (* cosTheta (+ (* cosTheta 1/2) -3/2)) -1))) cosTheta) (sqrt (PI)))))

rewrite295.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3164×	`-lowering-.f32`
3164×	`-lowering-.f64`
2524×	`/-lowering-/.f32`
2524×	`/-lowering-/.f64`
844×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	246
1	219	225
2	1052	225
3	6823	225
0	8012	225

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 857

Calls

Call 1

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

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

simplify425.0ms (3%)

Algorithm

1×	egg-herbie

Rules

5160×	`+-lowering-+.f64`
5160×	`+-lowering-+.f32`
4428×	`-lowering-.f32`
4428×	`-lowering-.f64`
1704×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	917	10468
1	3073	9209
0	8502	9209

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (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 (* (/ 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))
(* (/ 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 (* (/ 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))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
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c
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c
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
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(sqrt (/ 1 (PI)))
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(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))
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(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* -3/2 cosTheta)
(* cosTheta (- (* 1/2 cosTheta) 3/2))
(* cosTheta (- (* 1/2 cosTheta) 3/2))
(* cosTheta (- (* 1/2 cosTheta) 3/2))
(* 1/2 (pow cosTheta 2))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* 1/2 (pow cosTheta 2))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(sqrt (/ 1 (PI)))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* 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))))))
(* -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
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))) (neg.f32 cosTheta)) (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (neg.f32 (+.f32 (.f32 cosTheta (-.f32 (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32))) (.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))))) (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))))) (.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (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))))))))
(+.f32 (/.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))) (.f32 #s(literal -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (pow.f32 (+.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)) #s(literal 2 binary32))))))
(- (+ (* 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))))))))
(-.f32 (+.f32 (/.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))) (/.f32 #s(literal 1/4 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (.f32 (exp.f32 (+.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) #s(literal -2 binary32)) (pow.f32 (+.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)) #s(literal 3 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 (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 (+.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)) #s(literal 2 binary32))))) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (pow.f32 (+.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)) #s(literal 2 binary32)))) #s(literal 1/2 binary32))))
(- (+ (* -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))))))))
(-.f32 (-.f32 (+.f32 (/.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))) (/.f32 #s(literal 1/4 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (.f32 (exp.f32 (+.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) #s(literal -2 binary32)) (pow.f32 (+.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)) #s(literal 3 binary32)))))) (/.f32 (+.f32 (.f32 #s(literal 1/16 binary32) (+.f32 (/.f32 (sqrt.f32 (/.f32 (pow.f32 cosTheta #s(literal 5 binary32)) (PI.f32))) (.f32 (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32))) (pow.f32 (+.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)) #s(literal 2 binary32)))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (.f32 (exp.f32 (+.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 4 binary32))) (pow.f32 (+.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)) #s(literal 3 binary32)))))) (.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 cosTheta (PI.f32)))) (/.f32 (+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) cosTheta) (.f32 (PI.f32) (.f32 (.f32 (exp.f32 (+.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) #s(literal -2 binary32)) (pow.f32 (+.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)) #s(literal 3 binary32))))) (.f32 (/.f32 (sqrt.f32 (/.f32 (.f32 cosTheta (.f32 cosTheta cosTheta)) (PI.f32))) (.f32 (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 (+.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)) #s(literal 2 binary32)))) #s(literal 1/8 binary32))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (+.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)))))) (pow.f32 cosTheta #s(literal 6 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 (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32)))) (pow.f32 (+.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)) #s(literal 2 binary32))))) (.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (pow.f32 (+.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)) #s(literal 2 binary32)))) #s(literal 1/2 binary32))))
(/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (exp.f32 (.f32 cosTheta cosTheta)))))
(+ (* 1/2 (* (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)))))))))
(+.f32 (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (exp.f32 (.f32 cosTheta cosTheta))))) (.f32 #s(literal 1/2 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -1 binary32))) (.f32 (.f32 (exp.f32 (.f32 cosTheta cosTheta)) (sqrt.f32 #s(literal 2 binary32))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (exp.f32 (.f32 cosTheta cosTheta)))) #s(literal 2 binary32))))))
(- (/ 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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(/ (+ (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 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)
(* (/ 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)
(/.f32 #s(literal 1 binary32) cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta)
(* 1/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))
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(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (+ (* 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))))
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(* 1/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))
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(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta))) cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta)))
(/ 1 (+ 1 (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta) (sqrt (/ 1 (PI))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta))))
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(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta) (sqrt (/ 1 (PI))))) c))) c)
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(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta) (sqrt (/ 1 (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
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(/ 1 c)
(/.f32 #s(literal 1 binary32) c)
(* -1 (/ (- (+ (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)) 1) c))
(/.f32 (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.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)))) (*.f32 cosTheta c))) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta) (sqrt (/ 1 (PI))))) 2) c) (+ 1 (* (/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
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(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2)))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
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(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 2 binary32) (.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) (*.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
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(/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) (pow cosTheta 2)))))) (pow cosTheta 2))
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(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
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(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
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(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
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(*.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 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(.f32 cosTheta (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32)))) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))))))
(* 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 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))) (+.f32 (.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))) (PI.f32))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (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 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 #s(literal -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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))))))
(* -1 (* 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (+.f32 (.f32 #s(literal 1/16 binary32) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))) (PI.f32))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))))) (.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32)))))))))
(* (/ 1 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 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (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 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI))))))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (*.f32 cosTheta cosTheta)))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))) cosTheta)))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) cosTheta)) cosTheta)))
(* -3/2 cosTheta)
(*.f32 cosTheta #s(literal -3/2 binary32))
(* cosTheta (- (* 1/2 cosTheta) 3/2))
(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))
(* cosTheta (- (* 1/2 cosTheta) 3/2))
(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))
(* cosTheta (- (* 1/2 cosTheta) 3/2))
(.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))
(* 1/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* 1/2 (pow cosTheta 2))
(.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 binary32) cosTheta)))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -3/2 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 cosTheta (.f32 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 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(.f32 cosTheta (+.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32)))) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))))))
(* 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 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (.f32 #s(literal 1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (sqrt.f32 #s(literal -2 binary32))))) (+.f32 (.f32 #s(literal 1/16 binary32) (/.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))) (PI.f32))) (pow.f32 (sqrt.f32 #s(literal -2 binary32)) #s(literal 5 binary32)))) (.f32 #s(literal -1/8 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (*.f32 #s(literal -2 binary32) (sqrt.f32 #s(literal -2 binary32))))))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(.f32 (.f32 (sqrt.f32 (/.f32 cosTheta (PI.f32))) (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 #s(literal 2 binary32))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(.f32 (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 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (*.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 #s(literal -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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (.f32 #s(literal -1/8 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 5 binary32))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (*.f32 #s(literal 2 binary32) (sqrt.f32 #s(literal 2 binary32))))))))
(* -1 (* 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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))) (.f32 #s(literal 1/2 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 #s(literal 2 binary32)))))) (+.f32 (.f32 #s(literal 1/16 binary32) (.f32 (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 7 binary32))) (PI.f32))) (/.f32 (sqrt.f32 #s(literal -1 binary32)) (pow.f32 (sqrt.f32 #s(literal 2 binary32)) #s(literal 5 binary32))))) (.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)))))))))

eval178.0ms (1.3%)

Compiler: Compiled 40102 to 5149 computations (87.2% saved)

prune227.0ms (1.6%)

Pruning

34 alts after pruning (31 fresh and 3 done)

	Pruned	Kept	Total
New	1409	26	1435
Fresh	10	5	15
Picked	2	3	5
Done	0	0	0
Total	1421	34	1455

Accuracy

99.8%

Counts

1455 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.9%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	97.2%	(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.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)))) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (/.f32 (/.f32 (sqrt.f32 (.f32 (PI.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) c)))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.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))))))))
	96.0%	(/.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)))))
	97.4%	(/.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)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)))
✓	97.4%	(/.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)))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32)))))))
	37.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (sqrt.f32 (PI.f32)))))
▶	37.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (-.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	92.5%	(/.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) cosTheta))))
	61.2%	(/.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)))
	56.3%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)))) #s(literal 1 binary32)))
	93.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
▶	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
✓	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	96.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta))))
▶	10.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	56.3%	(/.f32 #s(literal 1 binary32) (*.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
✓	5.2%	(/.f32 #s(literal 1 binary32) c)
	96.5%	(.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)))))))
▶	93.5%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	93.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	90.0%	(exp.f32 (.f32 #s(literal -1 binary32) (log1p.f32 (+.f32 c (/.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)))) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))))
	90.8%	(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 1276 to 911 computations (28.6% saved)

simplify195.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

2438×	`fma-lowering-fma.f32`
2438×	`fma-lowering-fma.f64`
1946×	`-lowering-.f32`
1946×	`-lowering-.f64`
1596×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	44	341
1	110	341
2	271	325
3	814	325
4	2231	313
5	6571	313
0	8044	313

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize243.0ms (1.7%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.4%	(/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))
✓	accuracy	44.1%	(.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta)))
✓	accuracy	99.6%	(*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
✓	accuracy	98.3%	(/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
✓	accuracy	96.9%	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
✓	accuracy	99.7%	(*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.6%	(-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c))))
✓	accuracy	99.0%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
✓	accuracy	98.8%	(.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	100.0%	(+.f32 #s(literal 1 binary32) c)
✓	accuracy	99.7%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.8%	(/.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))) (PI.f32))
✓	accuracy	99.1%	(/.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	98.3%	(/.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

172.0ms

256×

valid

Compiler

Compiled 382 to 45 computations (88.2% saved)

Precisions

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

ival-div: 19.0ms (33.1% of total)

ival-mult: 14.0ms (24.4% of total)

ival-add: 7.0ms (12.2% of total)

ival-sub: 7.0ms (12.2% of total)

ival-sqrt: 6.0ms (10.4% of total)

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

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

const: 1.0ms (1.7% of total)

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

series44.0ms (0.3%)

Counts

24 → 360

Calls

Call 1

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

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

Calls

90 calls:

Time	Variable		Point	Expression
8.0ms	cosTheta	@	inf	(/ 1 (+ 1 (/ (sqrt (/ (- 1 (* cosTheta 2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
3.0ms	cosTheta	@	-inf	(/ 1 (+ 1 (/ (sqrt (/ (- 1 (* cosTheta 2)) (PI))) (* cosTheta (exp (* cosTheta cosTheta))))))
2.0ms	cosTheta	@	-inf	(* cosTheta (- (sqrt (PI)) (* cosTheta (* (PI) (+ 1 c)))))
2.0ms	c	@	inf	(+ (+ 1 c) (/ (* (* cosTheta cosTheta) (- 1/2 (/ (- 3/2 (/ (+ (/ 1 cosTheta) -1) cosTheta)) cosTheta))) (sqrt (PI))))
1.0ms	c	@	0	(/ 1 (+ (+ 1 c) (/ (* (* cosTheta cosTheta) (- 1/2 (/ (- 3/2 (/ (+ (/ 1 cosTheta) -1) cosTheta)) cosTheta))) (sqrt (PI)))))

rewrite333.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4232×	`-lowering-.f32`
4232×	`-lowering-.f64`
3014×	`/-lowering-/.f32`
3014×	`/-lowering-/.f64`
788×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	249
1	203	242
2	1024	228
3	7516	228
0	8258	228

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 919

Calls

Call 1

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

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

simplify362.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

5150×	`-lowering-.f32`
5150×	`-lowering-.f64`
3794×	`+-lowering-+.f64`
3794×	`+-lowering-+.f32`
1884×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	914	7540
1	3141	6668
0	8268	6668

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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

eval214.0ms (1.5%)

Compiler: Compiled 39837 to 6426 computations (83.9% saved)

prune295.0ms (2.1%)

Pruning

51 alts after pruning (47 fresh and 4 done)

	Pruned	Kept	Total
New	1632	27	1659
Fresh	6	20	26
Picked	3	2	5
Done	1	2	3
Total	1642	51	1693

Accuracy

100.0%

Counts

1693 → 51

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.1%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 (*.f32 (-.f32 #s(literal -1 binary32) c) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) (/.f32 #s(literal -1 binary32) cosTheta))
	93.1%	(/.f32 (-.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) (/.f32 #s(literal 1 binary32) cosTheta))
	95.9%	(/.f32 cosTheta (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c))))
	95.8%	(/.f32 cosTheta (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))
	10.8%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 cosTheta c)) cosTheta))
	93.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
▶	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.4%	(/.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)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)))
✓	97.4%	(/.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)))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32)))))))
	37.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (sqrt.f32 (PI.f32)))))
	43.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (.f32 cosTheta (-.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
	92.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (-.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	92.5%	(/.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) cosTheta))))
	61.2%	(/.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)))
	56.3%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)))) #s(literal 1 binary32)))
	93.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
▶	98.1%	(/.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))))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
▶	37.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
✓	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
✓	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	96.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
✓	10.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	95.5%	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))))
	56.3%	(/.f32 #s(literal 1 binary32) (*.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
	58.9%	(/.f32 #s(literal 1 binary32) (.f32 (neg.f32 c) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (neg.f32 c)) #s(literal -1 binary32))))
	31.6%	(/.f32 #s(literal 1 binary32) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) c)) #s(literal -1 binary32))))
	10.8%	(-.f32 #s(literal 1 binary32) c)
▶	96.5%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
	58.7%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c))))
	93.1%	(.f32 cosTheta (-.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	91.7%	(.f32 cosTheta (-.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal 2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	96.4%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))
	93.5%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))))
	93.3%	(.f32 cosTheta (.f32 (neg.f32 c) (+.f32 (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))) (neg.f32 c)) (.f32 cosTheta (PI.f32)))))
	92.9%	(.f32 cosTheta (.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	10.4%	(.f32 cosTheta (.f32 c (*.f32 cosTheta (neg.f32 (PI.f32)))))
	93.7%	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
	93.5%	(.f32 c (-.f32 (/.f32 (.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32)))) c) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	90.7%	(exp.f32 (.f32 #s(literal -1 binary32) (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)))))))
	90.0%	(exp.f32 (.f32 #s(literal -1 binary32) (log1p.f32 (+.f32 c (/.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)))) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))))
▶	10.8%	#s(literal 1 binary32)

Compiler

Compiled 1821 to 1281 computations (29.7% saved)

simplify184.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

1942×	`sum3-define`
1800×	`sum5-define`
1662×	`sum4-define`
1628×	`fma-lowering-fma.f32`
1628×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	315
1	95	307
2	191	300
3	510	300
4	1442	281
5	4589	281
0	8518	281

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize267.0ms (1.9%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
✓	accuracy	98.4%	(/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))
✓	accuracy	44.1%	(.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta)))
✓	accuracy	99.7%	(+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))
✓	accuracy	98.9%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
✓	accuracy	97.4%	(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c))))
✓	accuracy	99.9%	(+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	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 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32))))
✓	accuracy	99.1%	(/.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))))))
✓	accuracy	98.3%	(/.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))))
✓	accuracy	97.6%	(pow.f32 (/.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal 2 binary32)))) #s(literal -1/2 binary32))

Results

199.0ms

256×

valid

Compiler

Compiled 349 to 43 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-div: 22.0ms (24.9% of total)

ival-mult: 20.0ms (22.6% of total)

ival-add: 17.0ms (19.2% of total)

ival-pow: 15.0ms (17% of total)

ival-sub: 5.0ms (5.7% of total)

ival-exp: 4.0ms (4.5% of total)

ival-sqrt: 2.0ms (2.3% of total)

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

const: 1.0ms (1.1% of total)

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

series21.0ms (0.2%)

Counts

18 → 264

Calls

Call 1

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

Outputs
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (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 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)>
#<alt (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))>
#<alt (+ 1 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))))>
#<alt (+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2)))))))>
#<alt (+ 1 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 3))))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (pow (sqrt -2) 5))))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (* (exp (pow cosTheta 2)) (sqrt -2))))) (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))))))>
#<alt (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))))>
#<alt (+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2)))))))>
#<alt (+ 1 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (* (sqrt -1) (sqrt 2)) (exp (pow cosTheta 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (sqrt 2))))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (* (exp (pow cosTheta 2)) (pow (sqrt 2) 3))))))))>
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#<alt (* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))>
#<alt (* c cosTheta)>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))>
#<alt (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))>
#<alt (sqrt (/ 1 (PI)))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))>
#<alt (* -1 (* cosTheta (sqrt (/ 1 (PI)))))>
#<alt (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))>
#<alt (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))>
#<alt (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))>
#<alt (* -1 (* cosTheta (sqrt (/ 1 (PI)))))>
#<alt (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>
#<alt (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>
#<alt (* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))>
#<alt (/ 1 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 (* 1/2 (pow cosTheta 2))>
#<alt (* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))>
#<alt (* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))>
#<alt (* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (+ (* 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))))>
#<alt (* 1/2 (pow cosTheta 2))>
#<alt (* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))>
#<alt (* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))>
#<alt (* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta))) cosTheta))))>
#<alt (* cosTheta (sqrt (PI)))>
#<alt (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))>
#<alt (* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))>
#<alt (/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) (pow cosTheta 2)))))) (pow cosTheta 2))>
#<alt (* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))>
#<alt (/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (+ (* -4 (* (/ 1 cosTheta) (sqrt (PI)))) (* -3 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))) (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))) cosTheta)>
#<alt (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ 1 (pow cosTheta 2))))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ 1 (pow cosTheta 2)))))))>
#<alt (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)>
#<alt (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)>
#<alt (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI))))))))>
#<alt (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))>
#<alt (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))>
#<alt (PI)>
#<alt (+ (PI) (* 2 (* cosTheta (PI))))>
#<alt (+ (PI) (* cosTheta (- (* 4 (* cosTheta (PI))) (* -2 (PI)))))>
#<alt (+ (PI) (* cosTheta (- (* cosTheta (- (* 8 (* cosTheta (PI))) (* -4 (PI)))) (* -2 (PI)))))>
#<alt (* -1/2 (/ (PI) cosTheta))>
#<alt (/ (+ (* -1/2 (PI)) (* -1/4 (/ (PI) cosTheta))) cosTheta)>
#<alt (/ (- (+ (* -1/2 (PI)) (* -1/8 (/ (PI) (pow cosTheta 2)))) (* 1/4 (/ (PI) cosTheta))) cosTheta)>
#<alt (/ (- (+ (* -1/2 (PI)) (* -1/16 (/ (PI) (pow cosTheta 3)))) (+ (* 1/8 (/ (PI) (pow cosTheta 2))) (* 1/4 (/ (PI) cosTheta)))) cosTheta)>
#<alt (* -1/2 (/ (PI) cosTheta))>
#<alt (* -1 (/ (+ (* 1/4 (/ (PI) cosTheta)) (* 1/2 (PI))) cosTheta))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (PI) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (PI) cosTheta)) (* -1/8 (PI))) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))>
#<alt (/ 1 (pow cosTheta 2))>
#<alt (/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))>
#<alt (/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))>
#<alt (/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))>
#<alt (/ -1 cosTheta)>
#<alt (/ (- (/ 1 cosTheta) 1) cosTheta)>
#<alt (/ (- (/ 1 cosTheta) 1) cosTheta)>
#<alt (/ (- (/ 1 cosTheta) 1) cosTheta)>
#<alt (/ -1 cosTheta)>
#<alt (* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))>
#<alt (* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))>
#<alt (* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))>

Calls

66 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta	@	-inf	(/ 1 (+ (/ (- 1 cosTheta) (pow (PI) 1/2)) (* cosTheta (+ 1 c))))
1.0ms	cosTheta	@	-inf	(* (/ 1 (+ (/ (- 1 cosTheta) (pow (PI) 1/2)) (* cosTheta (+ 1 c)))) cosTheta)
1.0ms	c	@	inf	(/ 1 (+ (/ (- 1 cosTheta) (pow (PI) 1/2)) (* cosTheta (+ 1 c))))
1.0ms	cosTheta	@	0	(/ 1 (+ 1 (/ (* (* cosTheta cosTheta) (- 1/2 (/ (- 3/2 (/ (+ (/ 1 cosTheta) -1) cosTheta)) cosTheta))) (sqrt (PI)))))
1.0ms	cosTheta	@	inf	(/ 1 (+ 1 (/ (* (* cosTheta cosTheta) (- 1/2 (/ (- 3/2 (/ (+ (/ 1 cosTheta) -1) cosTheta)) cosTheta))) (sqrt (PI)))))

rewrite321.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3082×	`-lowering-.f32`
3082×	`-lowering-.f64`
2140×	`/-lowering-/.f32`
2140×	`/-lowering-/.f64`
1442×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	219
1	190	207
2	873	199
3	5546	199
0	8616	199

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 571

Calls

Call 1

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

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

simplify432.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

5364×	`-lowering-.f32`
5364×	`-lowering-.f64`
4390×	`+-lowering-+.f64`
4390×	`+-lowering-+.f32`
1602×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	988	6735
1	3400	5971
0	8303	5971

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (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))))))))))
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c
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(/ 1 (* c cosTheta))
(/ (+ (* -1 (/ (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)) c)) (/ 1 cosTheta)) c)
(/ (- (+ (/ 1 cosTheta) (/ (* (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* (pow c 2) cosTheta))) (+ (* (/ (- 1 cosTheta) (* c (pow cosTheta 2))) (sqrt (/ 1 (PI)))) (/ 1 (* c cosTheta)))) c)
(/ (- (+ (* -1 (/ (* (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 2) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* (pow c 3) (pow cosTheta 2)))) (/ 1 cosTheta)) (+ (* -1 (/ (* (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* (pow c 2) cosTheta))) (+ (* (/ (- 1 cosTheta) (* c (pow cosTheta 2))) (sqrt (/ 1 (PI)))) (/ 1 (* c cosTheta))))) c)
(/ 1 (* c cosTheta))
(* -1 (/ (- (+ (* (/ (- 1 cosTheta) (* c (pow cosTheta 2))) (sqrt (/ 1 (PI)))) (/ 1 (* c cosTheta))) (/ 1 cosTheta)) c))
(* -1 (/ (- (* -1 (/ (- (/ (* (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* c cosTheta)) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) c)) (/ 1 cosTheta)) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (* (pow (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) 2) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) (* c (pow cosTheta 2))) (/ (* (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) cosTheta)) c)) (+ (* (/ (- 1 cosTheta) (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta))) c)) (/ 1 cosTheta)) c))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (+ 1 c)))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 c))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 c))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 c))))))
(+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta)))
(+ cosTheta (+ (* c cosTheta) (* (sqrt (/ 1 (PI))) (- 1 cosTheta))))
(+ cosTheta (+ (* c cosTheta) (* (sqrt (/ 1 (PI))) (- 1 cosTheta))))
(+ cosTheta (+ (* c cosTheta) (* (sqrt (/ 1 (PI))) (- 1 cosTheta))))
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))
(* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))
(* c (+ cosTheta (+ (* (/ (- 1 cosTheta) c) (sqrt (/ 1 (PI)))) (/ cosTheta c))))
(* c cosTheta)
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ cosTheta (* (sqrt (/ 1 (PI))) (- 1 cosTheta))) c)))))
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
(* -1 (* cosTheta (sqrt (/ 1 (PI)))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(* -1 (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))))
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* cosTheta (- (* -3/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* 1/2 cosTheta) 3/2)) 1))) cosTheta)
(* 1/2 (pow cosTheta 2))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))
(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (+ (* 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))))
(* 1/2 (pow cosTheta 2))
(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))
(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta))) cosTheta))))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) (pow cosTheta 2)))))) (pow cosTheta 2))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (+ (* -4 (* (/ 1 cosTheta) (sqrt (PI)))) (* -3 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))) (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ 1 (pow cosTheta 2))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ 1 (pow cosTheta 2)))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI))))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(PI)
(+ (PI) (* 2 (* cosTheta (PI))))
(+ (PI) (* cosTheta (- (* 4 (* cosTheta (PI))) (* -2 (PI)))))
(+ (PI) (* cosTheta (- (* cosTheta (- (* 8 (* cosTheta (PI))) (* -4 (PI)))) (* -2 (PI)))))
(* -1/2 (/ (PI) cosTheta))
(/ (+ (* -1/2 (PI)) (* -1/4 (/ (PI) cosTheta))) cosTheta)
(/ (- (+ (* -1/2 (PI)) (* -1/8 (/ (PI) (pow cosTheta 2)))) (* 1/4 (/ (PI) cosTheta))) cosTheta)
(/ (- (+ (* -1/2 (PI)) (* -1/16 (/ (PI) (pow cosTheta 3)))) (+ (* 1/8 (/ (PI) (pow cosTheta 2))) (* 1/4 (/ (PI) cosTheta)))) cosTheta)
(* -1/2 (/ (PI) cosTheta))
(* -1 (/ (+ (* 1/4 (/ (PI) cosTheta)) (* 1/2 (PI))) cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (PI) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (PI) cosTheta)) (* -1/8 (PI))) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))
(/ 1 (pow cosTheta 2))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/ -1 cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/ -1 cosTheta)
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))

Outputs
(* cosTheta (sqrt (PI)))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 (*.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))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32))) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #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)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (.f32 (-.f32 (-.f32 (.f32 (PI.f32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32))) (.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.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)))))) (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)))))))))
(/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (/ (sqrt -2) (exp (pow cosTheta 2))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.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) (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)))))))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.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 -1/2 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (.f32 (.f32 (sqrt.f32 #s(literal -2 binary32)) (exp.f32 (.f32 cosTheta cosTheta))) (pow.f32 (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32)))) (sqrt.f32 #s(literal -2 binary32))) (exp.f32 (*.f32 cosTheta cosTheta)))) #s(literal 2 binary32))))))
(- (+ (* 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))))))))
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(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 c))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* (* cosTheta (pow (+ 1 c) 2)) (sqrt (pow (PI) 3))) (* (PI) (+ 1 c))))))
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(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (* (pow (PI) 2) (pow (+ 1 c) 3)))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 c) 2))))) (* (PI) (+ 1 c))))))
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(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
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(- (+ (* -1 (* (/ 1 (* (pow cosTheta 3) (pow (+ 1 c) 4))) (sqrt (/ 1 (pow (PI) 3))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (pow (+ 1 c) 3)))) (/ 1 (+ 1 c)))) (* (/ 1 (* cosTheta (pow (+ 1 c) 2))) (sqrt (/ 1 (PI)))))
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(/ 1 (+ 1 c))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
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(+ (* -1 (/ (- (* -1 (/ (+ (* -1 (* (/ 1 (* cosTheta (pow (+ 1 c) 4))) (sqrt (/ 1 (pow (PI) 3))))) (/ 1 (* (PI) (pow (+ 1 c) 3)))) cosTheta)) (* -1 (* (sqrt (/ 1 (PI))) (/ 1 (pow (+ 1 c) 2))))) cosTheta)) (/ 1 (+ 1 c)))
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(/ 1 (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
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(/.f32 #s(literal 1 binary32) c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) c))) c)
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(/ (- (+ 1 (/ (pow (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))) c)
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(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 2) (pow c 2))) (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c)))) c)
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(/.f32 #s(literal 1 binary32) c)
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(/.f32 (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta c)) (+.f32 (/.f32 #s(literal 1 binary32) c) #s(literal -1 binary32))) (neg.f32 c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 2) c) (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
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(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 3) c) (pow (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 2)) c)) (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1) c))
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(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 c))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c))) cosTheta)
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c
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))))
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c
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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)))))))
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(/ (+ 1 (* -1 cosTheta)) cosTheta)
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(* 1/2 (pow cosTheta 2))
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(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
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(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (/ 1 cosTheta)) cosTheta))))
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(* (pow cosTheta 2) (- (+ 1/2 (/ 1 (pow cosTheta 3))) (+ (* 3/2 (/ 1 cosTheta)) (/ 1 (pow cosTheta 2)))))
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(* 1/2 (pow cosTheta 2))
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(* (pow cosTheta 2) (- 1/2 (* 3/2 (/ 1 cosTheta))))
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(* (pow cosTheta 2) (+ 1/2 (* -1 (/ (+ 3/2 (* -1 (/ (- (/ 1 cosTheta) 1) cosTheta))) cosTheta))))
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(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 (neg.f32 cosTheta) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32))))) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))))) (+ (* 1/2 (sqrt (PI))) (* 3/2 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))) (+ (* -3/2 (sqrt (PI))) (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(.f32 cosTheta (+.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (-.f32 (.f32 cosTheta (-.f32 (neg.f32 (.f32 cosTheta (-.f32 (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 1/2 binary32)) (.f32 (.f32 #s(literal 3/2 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 (.f32 (sqrt.f32 (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)))))))) (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -3/2 binary32)) (.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (-.f32 #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)))))))))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 2 binary32) (.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) (*.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) (pow cosTheta 2))) (* 2 (sqrt (PI)))) (* -6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32)) (.f32 (.f32 (PI.f32) #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))) (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 2 binary32) (.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta))))) (.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (+ (* 3 (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (+ (* 4 (sqrt (PI))) (* 12 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) (pow cosTheta 3))) (* 2 (sqrt (PI)))) (+ (* -18 (* (/ 1 (pow cosTheta 2)) (sqrt (PI)))) (+ (* -6 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) (pow cosTheta 2)))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2 binary32)) (/.f32 (+.f32 (.f32 #s(literal 3 binary32) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32)) (.f32 (.f32 (PI.f32) #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 4 binary32)) (.f32 (.f32 #s(literal 12 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (.f32 #s(literal -18 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 #s(literal -6 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) (/.f32 (.f32 (.f32 (PI.f32) #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(* 2 (* (/ 1 (pow cosTheta 2)) (sqrt (PI))))
(.f32 #s(literal 2 binary32) (/.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta)))
(/ (+ (* 2 (sqrt (PI))) (* 6 (* (/ 1 cosTheta) (sqrt (PI))))) (pow cosTheta 2))
(/.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 #s(literal 2 binary32) (.f32 #s(literal 6 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))) (*.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- (+ (* -18 (* (/ 1 cosTheta) (sqrt (PI)))) (* 4 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) cosTheta))) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2 binary32)) (/.f32 (+.f32 (.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -18 binary32)) (+.f32 (/.f32 (.f32 (.f32 (PI.f32) #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (.f32 (sqrt.f32 (PI.f32)) #s(literal -6 binary32)))) cosTheta)) (.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -12 (/ (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (+ (* -4 (* (/ 1 cosTheta) (sqrt (PI)))) (* -3 (/ (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))) (+ (* -18 (sqrt (PI))) (* 4 (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)) (* 6 (sqrt (PI)))) cosTheta)) (* 2 (sqrt (PI)))) (pow cosTheta 2))
(/.f32 (-.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal 2 binary32)) (/.f32 (+.f32 (/.f32 (-.f32 (+.f32 (+.f32 (/.f32 (.f32 #s(literal -12 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta) (.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) #s(literal -4 binary32))) (/.f32 (.f32 #s(literal -3 binary32) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32)) (.f32 (.f32 (PI.f32) #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)) (+.f32 (.f32 (sqrt.f32 (PI.f32)) #s(literal -18 binary32)) (.f32 (.f32 (PI.f32) #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) #s(literal -6 binary32))) cosTheta)) (*.f32 cosTheta cosTheta))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) (-.f32 (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1/2 binary32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ 1 (pow cosTheta 2))))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1/2 binary32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (/ 1 (pow cosTheta 2)))))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))))) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1/2 binary32))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)) cosTheta)))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) cosTheta)) cosTheta)))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (*.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (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 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32)))))) cosTheta)
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1/2 binary32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1/2 binary32))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI))))))))
(.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (*.f32 cosTheta cosTheta)))))))
(* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
(* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1/2 binary32))))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* 3/2 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 3/2 binary32))) cosTheta)))
(* (pow cosTheta 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI))))) cosTheta)) (* 1/2 (sqrt (/ 1 (PI))))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 1/2 binary32)) (/.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal 3/2 binary32)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) cosTheta)) cosTheta)))
(PI)
(PI.f32)
(+ (PI) (* 2 (* cosTheta (PI))))
(.f32 (+.f32 (.f32 #s(literal 2 binary32) cosTheta) #s(literal 1 binary32)) (PI.f32))
(+ (PI) (* cosTheta (- (* 4 (* cosTheta (PI))) (* -2 (PI)))))
(+.f32 (PI.f32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 (*.f32 #s(literal 4 binary32) cosTheta) #s(literal 2 binary32)))))
(+ (PI) (* cosTheta (- (* cosTheta (- (* 8 (* cosTheta (PI))) (* -4 (PI)))) (* -2 (PI)))))
(+.f32 (PI.f32) (.f32 cosTheta (+.f32 (.f32 cosTheta (.f32 (PI.f32) (+.f32 (.f32 #s(literal 8 binary32) cosTheta) #s(literal 4 binary32)))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
(* -1/2 (/ (PI) cosTheta))
(/.f32 (*.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)
(/ (+ (* -1/2 (PI)) (* -1/4 (/ (PI) cosTheta))) cosTheta)
(/.f32 (+.f32 (.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (.f32 (PI.f32) #s(literal -1/4 binary32)) cosTheta)) cosTheta)
(/ (- (+ (* -1/2 (PI)) (* -1/8 (/ (PI) (pow cosTheta 2)))) (* 1/4 (/ (PI) cosTheta))) cosTheta)
(/.f32 (+.f32 (.f32 (PI.f32) #s(literal -1/2 binary32)) (+.f32 (.f32 #s(literal -1/8 binary32) (/.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 (.f32 (PI.f32) #s(literal -1/4 binary32)) cosTheta))) cosTheta)
(/ (- (+ (* -1/2 (PI)) (* -1/16 (/ (PI) (pow cosTheta 3)))) (+ (* 1/8 (/ (PI) (pow cosTheta 2))) (* 1/4 (/ (PI) cosTheta)))) cosTheta)
(/.f32 (+.f32 (.f32 (PI.f32) #s(literal -1/2 binary32)) (-.f32 (/.f32 (.f32 #s(literal -1/16 binary32) (PI.f32)) (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 (/.f32 (.f32 (PI.f32) #s(literal 1/4 binary32)) cosTheta) (.f32 #s(literal 1/8 binary32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))) cosTheta)
(* -1/2 (/ (PI) cosTheta))
(/.f32 (*.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)
(* -1 (/ (+ (* 1/4 (/ (PI) cosTheta)) (* 1/2 (PI))) cosTheta))
(/.f32 (+.f32 (/.f32 (.f32 (PI.f32) #s(literal 1/4 binary32)) cosTheta) (.f32 (PI.f32) #s(literal 1/2 binary32))) (neg.f32 cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (PI) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))
(/.f32 (-.f32 (.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (+.f32 (/.f32 (.f32 (PI.f32) #s(literal -1/8 binary32)) cosTheta) (*.f32 (PI.f32) #s(literal -1/4 binary32))) cosTheta)) (neg.f32 cosTheta))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (PI) cosTheta)) (* -1/8 (PI))) cosTheta)) (* 1/4 (PI))) cosTheta)) (* 1/2 (PI))) cosTheta))
(/.f32 (-.f32 (.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (+.f32 (/.f32 (+.f32 (/.f32 (.f32 #s(literal 1/16 binary32) (PI.f32)) cosTheta) (.f32 (PI.f32) #s(literal 1/8 binary32))) (neg.f32 cosTheta)) (.f32 (PI.f32) #s(literal -1/4 binary32))) cosTheta)) (neg.f32 cosTheta))
(/ 1 (pow cosTheta 2))
(/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))
(/ (+ 1 (* -1 cosTheta)) (pow cosTheta 2))
(/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (*.f32 cosTheta cosTheta))
(/ -1 cosTheta)
(/.f32 #s(literal -1 binary32) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
(/ (- (/ 1 cosTheta) 1) cosTheta)
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)
(/ -1 cosTheta)
(/.f32 #s(literal -1 binary32) cosTheta)
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(/.f32 (*.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) cosTheta)
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(/.f32 (*.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) cosTheta)
(* -1 (/ (- 1 (/ 1 cosTheta)) cosTheta))
(/.f32 (*.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) cosTheta)

eval112.0ms (0.8%)

Compiler: Compiled 20738 to 3294 computations (84.1% saved)

prune155.0ms (1.1%)

Pruning

52 alts after pruning (44 fresh and 8 done)

	Pruned	Kept	Total
New	823	12	835
Fresh	10	32	42
Picked	1	4	5
Done	0	4	4
Total	834	52	886

Accuracy

100.0%

Counts

886 → 52

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.1%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 (*.f32 (-.f32 #s(literal -1 binary32) c) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) (/.f32 #s(literal -1 binary32) cosTheta))
	93.1%	(/.f32 (-.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) (/.f32 #s(literal 1 binary32) cosTheta))
	95.9%	(/.f32 cosTheta (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c))))
	95.8%	(/.f32 cosTheta (+.f32 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta))))
	10.8%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 cosTheta c)) cosTheta))
	93.0%	(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
	95.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))) cosTheta))
	93.1%	(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
✓	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
	93.5%	(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (+.f32 #s(literal 1 binary32) c)))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (sqrt.f32 (PI.f32)))))
	97.4%	(/.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)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)))
✓	97.4%	(/.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)))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (-.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
	92.5%	(/.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) cosTheta))))
	61.2%	(/.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)))
	56.3%	(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)))) #s(literal 1 binary32)))
	93.2%	(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
✓	98.1%	(/.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))))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	97.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
	93.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (sqrt.f32 (PI.f32)))))
	43.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (*.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta)) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
	43.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta (+.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))))
	37.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (sqrt.f32 (PI.f32)))))
✓	37.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
✓	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal 2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))
	93.0%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
✓	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -2 binary32))) (PI.f32))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))
	96.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta))))
	95.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))
✓	10.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
	56.3%	(/.f32 #s(literal 1 binary32) (*.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
	10.8%	(-.f32 #s(literal 1 binary32) c)
	96.5%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
	96.4%	(.f32 (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)
	96.5%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 c (+.f32 (+.f32 cosTheta (/.f32 cosTheta c)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)
	58.7%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c))))
	93.7%	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
	93.1%	(.f32 cosTheta (-.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	91.7%	(.f32 cosTheta (-.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal 2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	93.5%	(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))))
	93.3%	(.f32 cosTheta (.f32 (neg.f32 c) (+.f32 (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))) (neg.f32 c)) (.f32 cosTheta (PI.f32)))))
	92.9%	(.f32 cosTheta (.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
	10.4%	(.f32 cosTheta (.f32 c (*.f32 cosTheta (neg.f32 (PI.f32)))))
	93.5%	(.f32 c (-.f32 (/.f32 (.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32)))) c) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	90.7%	(exp.f32 (.f32 #s(literal -1 binary32) (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)))))))
	36.2%	(exp.f32 (.f32 #s(literal -1 binary32) (log1p.f32 (/.f32 (.f32 cosTheta cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta)))))))
✓	10.8%	#s(literal 1 binary32)

Compiler

Compiled 2482 to 1062 computations (57.2% saved)

regimes179.0ms (1.3%)

Counts

87 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

51.0ms	(+.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))))
26.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
26.0ms	c
23.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
22.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta`
98.3%	1	`c`
98.3%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.3%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.3%	1	`(+.f32 #s(literal 1 binary32) c)`
98.3%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`

Compiler

Compiled 84 to 58 computations (31% saved)

regimes107.0ms (0.8%)

Counts

74 → 1

Calls

Call 1

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

Calls

3 calls:

58.0ms	(+.f32 #s(literal 1 binary32) c)
20.0ms	cosTheta
20.0ms	c

Results

Accuracy	Segments	Branch
98.3%	1	`c`
98.3%	1	`(+.f32 #s(literal 1 binary32) c)`
98.3%	1	`cosTheta`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes66.0ms (0.5%)

Counts

72 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(-.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
(.f32 cosTheta (.f32 c (*.f32 cosTheta (neg.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 cosTheta c)) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (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 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) 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) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (+.f32 #s(literal 1 binary32) c)))
(.f32 cosTheta (.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 #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 cosTheta (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c))))
(/.f32 (-.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
(.f32 c (-.f32 (/.f32 (.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32)))) c) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(.f32 cosTheta (.f32 (neg.f32 c) (+.f32 (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))) (neg.f32 c)) (.f32 cosTheta (PI.f32)))))
(/.f32 #s(literal 1 binary32) (*.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))))
(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 (*.f32 (-.f32 #s(literal -1 binary32) c) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) (/.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) (.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 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 c (+.f32 (+.f32 cosTheta (/.f32 cosTheta c)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)
(/.f32 #s(literal 1 binary32) (.f32 (neg.f32 c) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (neg.f32 c)) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta (+.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) 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) (.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 (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.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))))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.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)))) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #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 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta)) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (-.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.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) (/.f32 (.f32 cosTheta (-.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) c)) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(.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 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal 2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(.f32 cosTheta (-.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32)))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(.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)))))))
(/.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 (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 (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))
(/.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))))))

Outputs

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

Calls

3 calls:

23.0ms	cosTheta
19.0ms	c
17.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes94.0ms (0.7%)

Counts

68 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)
(-.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) c)
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) c))
(.f32 cosTheta (.f32 c (*.f32 cosTheta (neg.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (*.f32 cosTheta c)) cosTheta))
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 c (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) (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 cosTheta (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) 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) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (+.f32 #s(literal 1 binary32) c)))
(.f32 cosTheta (.f32 cosTheta (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (sqrt.f32 (PI.f32)) cosTheta) (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 cosTheta (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)))) cosTheta)
(/.f32 #s(literal 1 binary32) (+.f32 #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 cosTheta (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (*.f32 cosTheta (+.f32 #s(literal 1 binary32) c))))
(/.f32 (-.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) (/.f32 #s(literal 1 binary32) cosTheta))
(/.f32 #s(literal 1 binary32) (+.f32 (.f32 c (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta c)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
(.f32 c (-.f32 (/.f32 (.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32)))) c) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(.f32 cosTheta (.f32 (neg.f32 c) (+.f32 (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (PI.f32))) (neg.f32 c)) (.f32 cosTheta (PI.f32)))))
(/.f32 #s(literal 1 binary32) (*.f32 (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) (neg.f32 c)) #s(literal -1 binary32)) (neg.f32 c)))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal -3/2 binary32)) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 cosTheta (+.f32 (.f32 cosTheta c) (.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (-.f32 #s(literal 1 binary32) cosTheta))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))) cosTheta)
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 cosTheta (+.f32 #s(literal 1 binary32) c)))))
(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 (*.f32 (-.f32 #s(literal -1 binary32) c) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))) (/.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) (.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 cosTheta (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))) cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 c (+.f32 (+.f32 cosTheta (/.f32 cosTheta c)) (/.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal 1 binary32) cosTheta)) c)))) cosTheta)
(/.f32 #s(literal 1 binary32) (.f32 (neg.f32 c) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (neg.f32 c)) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta (+.f32 (.f32 cosTheta (+.f32 (.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)) cosTheta)) cosTheta))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta (+.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) 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) (.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 (+.f32 (*.f32 cosTheta #s(literal 1/2 binary32)) #s(literal -3/2 binary32))) #s(literal -1 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) cosTheta)))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 cosTheta (+.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))))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 #s(literal 1 binary32) c) (/.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)))) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1/2 binary32) (/.f32 (-.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #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 1/2 binary32) (/.f32 (-.f32 #s(literal -3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta)) (/.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 cosTheta (-.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))))
(/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.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) (/.f32 (.f32 cosTheta (-.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal 3/2 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) cosTheta)) cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (/.f32 #s(literal 1 binary32) cosTheta))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (.f32 (neg.f32 c) (+.f32 (neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal 1/2 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta cosTheta))) (+.f32 (/.f32 #s(literal 3/2 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))))) c)) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal -3/2 binary32)) cosTheta) (+.f32 #s(literal 1 binary32) c)))
(.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 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) #s(literal 2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(.f32 cosTheta (-.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3/2 binary32)) (.f32 cosTheta (*.f32 (PI.f32) (+.f32 #s(literal 1 binary32) c)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (*.f32 (PI.f32) (log.f32 (E.f32)))))))
(.f32 cosTheta (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (*.f32 (PI.f32) (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))))
(.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)))))))

Outputs

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

Calls

3 calls:

46.0ms	cosTheta
23.0ms	(+.f32 #s(literal 1 binary32) c)
18.0ms	c

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes49.0ms (0.3%)

Counts

56 → 1

Calls

Call 1

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

16.0ms	c
15.0ms	cosTheta
14.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes45.0ms (0.3%)

Counts

50 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

15.0ms	c
15.0ms	cosTheta
11.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes43.0ms (0.3%)

Counts

46 → 1

Calls

Call 1

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

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:

16.0ms	cosTheta
13.0ms	c
11.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.0%	1	`cosTheta`
97.0%	1	`c`
97.0%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes37.0ms (0.3%)

Counts

42 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

12.0ms	c
12.0ms	cosTheta
9.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
97.0%	1	`cosTheta`
97.0%	1	`(+.f32 #s(literal 1 binary32) c)`
97.0%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes35.0ms (0.2%)

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.5%	1	`cosTheta`
96.5%	1	`c`
96.5%	1	`(+.f32 #s(literal 1 binary32) c)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes30.0ms (0.2%)

Counts

33 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	c
9.0ms	cosTheta
7.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes28.0ms (0.2%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	(+.f32 #s(literal 1 binary32) c)
9.0ms	cosTheta
7.0ms	c

Results

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes15.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	cosTheta
5.0ms	c
4.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
93.7%	1	`cosTheta`
93.7%	1	`(+.f32 #s(literal 1 binary32) c)`
93.7%	1	`c`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes28.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

23.0ms	cosTheta
2.0ms	c
2.0ms	(+.f32 #s(literal 1 binary32) c)

Results

Accuracy	Segments	Branch
10.8%	1	`c`
10.8%	1	`(+.f32 #s(literal 1 binary32) c)`
10.8%	1	`cosTheta`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary32)

Outputs
#s(literal 1 binary32)

Calls

2 calls:

1.0ms	cosTheta
1.0ms	c

Results

Accuracy	Segments	Branch
10.8%	1	`c`
10.8%	1	`cosTheta`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	224
1	129	224
2	151	224
3	167	224
4	186	224
5	197	224
6	212	224
7	219	224
8	223	224
9	224	224

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness3.4s (24.1%)

Rules

6418×	`-lowering-.f32`
6418×	`-lowering-.f64`
5364×	`-lowering-.f32`
5364×	`-lowering-.f64`
5160×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	914	7540
1	3141	6668
0	8268	6668
0	917	10468
1	3073	9209
0	8502	9209
0	45	246
1	219	225
2	1052	225
3	6823	225
0	8012	225
0	29	149
1	138	143
2	734	126
3	3953	126
0	8500	126
0	988	6735
1	3400	5971
0	8303	5971
0	44	249
1	203	242
2	1024	228
3	7516	228
0	8258	228
0	734	7080
1	2383	6250
0	8491	6250
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×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 656 to 406 computations (38.1% saved)

preprocess90.0ms (0.6%)

Compiler: Compiled 506 to 196 computations (61.3% saved)

Iter	Nodes	Cost
0	80	224
1	129	224
2	151	224
3	167	224
4	186	224
5	197	224
6	212	224
7	219	224
8	223	224
9	224	224

Iter	Nodes	Cost
0	80	224
1	129	224
2	151	224
3	167	224
4	186	224
5	197	224
6	212	224
7	219	224
8	223	224
9	224	224

analyze41.0ms (0.3%)

sample2.5s (17.7%)

preprocess266.0ms (1.9%)

explain242.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify186.0ms (1.3%)

localize344.0ms (2.5%)

series127.0ms (0.9%)

rewrite617.0ms (4.4%)

simplify387.0ms (2.8%)

eval103.0ms (0.7%)

prune188.0ms (1.3%)

simplify159.0ms (1.1%)

localize264.0ms (1.9%)

series36.0ms (0.3%)

rewrite295.0ms (2.1%)

simplify425.0ms (3%)

eval178.0ms (1.3%)

prune227.0ms (1.6%)

simplify195.0ms (1.4%)

localize243.0ms (1.7%)

series44.0ms (0.3%)

rewrite333.0ms (2.4%)

simplify362.0ms (2.6%)

eval214.0ms (1.5%)

prune295.0ms (2.1%)

simplify184.0ms (1.3%)

localize267.0ms (1.9%)

series21.0ms (0.2%)

rewrite321.0ms (2.3%)

simplify432.0ms (3.1%)

eval112.0ms (0.8%)

prune155.0ms (1.1%)

regimes179.0ms (1.3%)

regimes107.0ms (0.8%)

regimes66.0ms (0.5%)

regimes94.0ms (0.7%)

regimes49.0ms (0.3%)

regimes45.0ms (0.3%)

regimes43.0ms (0.3%)

regimes37.0ms (0.3%)

regimes35.0ms (0.2%)

regimes30.0ms (0.2%)

regimes28.0ms (0.2%)

regimes15.0ms (0.1%)

regimes28.0ms (0.2%)

regimes3.0ms (0%)

simplify38.0ms (0.3%)

soundness3.4s (24.1%)

preprocess90.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	80	224
1	129	224
2	151	224
3	167	224
4	186	224
5	197	224
6	212	224
7	219	224
8	223	224
9	224	224