Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze35.0ms (0.6%)

Memory

-3.4MiB live, 39.6MiB allocated; 13ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample1.6s (29.4%)

Memory

72.9MiB live, 2 806.7MiB allocated; 492ms collecting garbage

Samples

1.3s	8 256×	0	valid
10.0ms	64×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-div: 234.0ms (23.3% of total)

ival-mult: 212.0ms (21.1% of total)

ival-add: 164.0ms (16.3% of total)

ival-sqrt: 108.0ms (10.7% of total)

ival-sub: 98.0ms (9.7% of total)

ival-exp: 96.0ms (9.5% of total)

ival-pi: 42.0ms (4.2% of total)

ival-neg: 35.0ms (3.5% of total)

exact: 8.0ms (0.8% of total)

adjust: 3.0ms (0.3% of total)

ival-assert: 2.0ms (0.2% of total)

const: 2.0ms (0.2% of total)

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

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

Bogosity

explain262.0ms (4.7%)

Memory

23.2MiB live, 442.2MiB allocated; 92ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

63.0ms

512×

valid

Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-div: 10.0ms (22.1% of total)

ival-mult: 9.0ms (19.9% of total)

ival-sqrt: 7.0ms (15.5% of total)

ival-add: 5.0ms (11.1% of total)

ival-sub: 5.0ms (11.1% of total)

ival-exp: 4.0ms (8.8% of total)

ival-neg: 3.0ms (6.6% of total)

ival-pi: 2.0ms (4.4% of total)

ival-true: 1.0ms (2.2% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

preprocess181.0ms (3.3%)

Memory

-5.7MiB live, 231.7MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	158
1	144	142
2	491	134
3	2194	132
0	18	25
0	33	25
1	60	23
2	173	22
3	742	22
4	3742	22
0	8784	21

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Compiler

Compiled 25 to 18 computations (28% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

97.8%

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

Compiler

Compiled 25 to 18 computations (28% saved)

series48.0ms (0.9%)

Memory

6.3MiB live, 56.3MiB allocated; 4ms collecting garbage

Counts

18 → 111

Calls

Call 1

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

Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 1))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx (- 1 cosTheta) #s(hole binary32 1))
#s(approx (- 1 cosTheta) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))))
#s(approx (* (neg cosTheta) cosTheta) #s(hole binary32 (* -1 (pow cosTheta 2))))
#s(approx (neg cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (+ (* -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)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -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))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole 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))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole 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)))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* (sqrt cosTheta) (sqrt -2))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* -2 cosTheta)))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 2))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (- 1 cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 1))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (exp (* -1 (pow cosTheta 2)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (- (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 5) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 4) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3))))) (* 1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (+ (* 1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))) (* (sqrt 2) (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (sqrt 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (+ (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* (pow (sqrt 2) 3) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 2))))) (* 1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt 2) 2) (pow (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))) 3)))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* (sqrt cosTheta) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -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)))))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 (* cosTheta (- 1 (/ 1 cosTheta))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (+ 1 c) #s(hole binary32 1))
#s(approx (+ 1 c) #s(hole binary32 (+ 1 c)))
#s(approx c #s(hole binary32 c))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ (- (+ 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)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 c))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ 1 c) #s(hole binary32 c))
#s(approx (+ 1 c) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* -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))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	cosTheta	@	inf	((/ 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))
10.0ms	cosTheta	@	-inf	((/ 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))
3.0ms	cosTheta	@	0	((/ 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))
3.0ms	c	@	0	((/ 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))
1.0ms	c	@	inf	((/ 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))

rewrite157.0ms (2.8%)

Memory

2.9MiB live, 141.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	634	6295
0	657	5601
0	3783	5289

Stop Event

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

Counts

129 → 177

Calls

Call 1

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

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

eval27.0ms (0.5%)

Memory: -14.2MiB live, 35.8MiB allocated; 6ms collecting garbage
Compiler: Compiled 8 637 to 1 127 computations (87% saved)

prune17.0ms (0.3%)

Memory

-11.5MiB live, 35.3MiB allocated; 2ms collecting garbage

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	170	18	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	18	189

Accuracy

99.3%

Counts

189 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	97.4%	(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
▶	96.6%	(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
	95.3%	(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (fma.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	95.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	92.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	95.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
▶	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (+.f32 (fma.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32) (.f32 (.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) c) #s(literal 1 binary32)) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
	55.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
▶	5.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	96.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (*.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
▶	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	93.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))

Compiler

Compiled 1 414 to 940 computations (33.5% saved)

series54.0ms (1%)

Memory

12.9MiB live, 103.6MiB allocated; 12ms collecting garbage

Counts

51 → 320

Calls

Call 1

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

Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 1))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))))
#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 1))
#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1)))))
#s(approx (exp (* (neg cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1)))))
#s(approx (* (neg cosTheta) cosTheta) #s(hole binary32 (* -1 (pow cosTheta 2))))
#s(approx (neg cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (* 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)))))))))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (sqrt (PI))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (/ (+ (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)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)))
#s(approx (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 cosTheta)) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)))
#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 1))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1)))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1)))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 1))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx (- 1 cosTheta) #s(hole binary32 1))
#s(approx (- 1 cosTheta) #s(hole binary32 (+ 1 (* -1 cosTheta))))
#s(approx (+ (* (neg cosTheta) cosTheta) 1) #s(hole binary32 1))
#s(approx (+ (* (neg cosTheta) cosTheta) 1) #s(hole binary32 (+ 1 (* -1 (pow cosTheta 2)))))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))) (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (sqrt (/ 1 (PI)))))
#s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 (+ c (* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* 1/2 (* cosTheta (sqrt (/ 1 (PI))))))))) (sqrt (/ 1 (PI))))))))
#s(approx (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) #s(hole binary32 (- (+ 1 c) (sqrt (/ 1 (PI))))))
#s(approx (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) #s(hole binary32 (- (+ 1 (+ c (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))))) (sqrt (/ 1 (PI))))))
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#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))))))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(hole binary32 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))))))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* -2 cosTheta)))
#s(approx (- (- 1 cosTheta) cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 2))))
#s(approx (- 1 cosTheta) #s(hole binary32 (* -1 cosTheta)))
#s(approx (- 1 cosTheta) #s(hole binary32 (* cosTheta (- (/ 1 cosTheta) 1))))
#s(approx (+ (* (neg cosTheta) cosTheta) 1) #s(hole binary32 (* -1 (pow cosTheta 2))))
#s(approx (+ (* (neg cosTheta) cosTheta) 1) #s(hole binary32 (* (pow cosTheta 2) (- (/ 1 (pow cosTheta 2)) 1))))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))))
#s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))))
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#s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (* (pow cosTheta 3) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (* (pow cosTheta 3) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (* (/ 1 (pow cosTheta 3)) (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2)))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))))
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#s(approx (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) #s(hole binary32 (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))))
#s(approx (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) #s(hole binary32 (* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (+ (/ 1 (pow cosTheta 2)) (/ c (pow cosTheta 2))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))))
#s(approx (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) #s(hole binary32 (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))))
#s(approx (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) #s(hole binary32 (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))))
#s(approx (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) #s(hole binary32 (* (pow cosTheta 2) (- (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* 1/2 (sqrt (/ 1 (PI)))) (/ c (pow cosTheta 2)))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) #s(hole binary32 (* 1/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))))
#s(approx (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) #s(hole binary32 (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) #s(hole binary32 (* (pow cosTheta 2) (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* -1 (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI)))))))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) #s(hole binary32 (* 1/2 (* cosTheta (sqrt (/ 1 (PI)))))))
#s(approx (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) #s(hole binary32 (* cosTheta (+ (* -3/2 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* 1/2 (sqrt (/ 1 (PI))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) #s(hole binary32 (/ 1 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))))
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#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
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#s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) #s(hole binary32 (+ 1 (+ c (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))))))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
#s(approx (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) #s(hole 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)))))))
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#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3))))))))
#s(approx (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) #s(hole binary32 (+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (* -1 (* (sqrt cosTheta) (* (sqrt -1) (sqrt 2))))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (* -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)))))))))
#s(approx (sqrt (+ (* -2 cosTheta) 1)) #s(hole binary32 (* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow cosTheta 7))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))))))))
#s(approx (+ (* -2 cosTheta) 1) #s(hole binary32 (* -1 (* cosTheta (- 2 (/ 1 cosTheta))))))
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Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	cosTheta	@	inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) -3/2 (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta) (* 1/2 (/ 1 (sqrt (PI)))) 1/2 (neg (/ 1 (sqrt (PI)))))
8.0ms	c	@	-inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) -3/2 (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta) (* 1/2 (/ 1 (sqrt (PI)))) 1/2 (neg (/ 1 (sqrt (PI)))))
8.0ms	cosTheta	@	0	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg 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) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) -3/2 (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta) (* 1/2 (/ 1 (sqrt (PI)))) 1/2 (neg (/ 1 (sqrt (PI)))))
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rewrite263.0ms (4.8%)

Memory

10.9MiB live, 344.6MiB allocated; 75ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1207	17715
0	1288	15074
1	7038	15074
0	8278	14537

Stop Event

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

Counts

371 → 613

Calls

Call 1

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

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

eval74.0ms (1.3%)

Memory: -29.6MiB live, 161.1MiB allocated; 16ms collecting garbage
Compiler: Compiled 32 608 to 3 375 computations (89.6% saved)

prune37.0ms (0.7%)

Memory

3.1MiB live, 103.0MiB allocated; 4ms collecting garbage

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	580	23	603
Fresh	8	5	13
Picked	4	1	5
Done	0	0	0
Total	592	29	621

Accuracy

99.7%

Counts

621 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	96.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #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) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
	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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	97.4%	(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	95.3%	(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (neg cosTheta) cosTheta) 1) #s(literal 1 binary32))))))
	95.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	92.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	96.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (.f32 (+.f32 (fma.f32 cosTheta (/.f32 (-.f32 (fma.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32))) cosTheta (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) cosTheta #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta) c)) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
	33.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (.f32 (fma.f32 (/.f32 (-.f32 (neg.f32 (/.f32 (-.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) cosTheta) #s(literal -1 binary32) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta cosTheta)))))
	54.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (.f32 (-.f32 (+.f32 (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) c) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (fma.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 (PI.f32))) cosTheta (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))) cosTheta #s(literal 1 binary32)) c)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) c))))
✓	5.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	89.0%	(exp.f32 (.f32 (log1p.f32 (+.f32 c (.f32 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))))) #s(literal -1 binary32)))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (.f32 (*.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
	96.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32) (neg.f32 (.f32 (pow.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
▶	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (* (/ 1 (sqrt (PI))) -1) c) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	93.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 #s(approx (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) c) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
▶	93.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	95.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))
▶	95.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 cosTheta) (PI.f32) (fma.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)) (/.f32 (.f32 (neg.f32 cosTheta) (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (PI.f32))) c))) c)) cosTheta))
	95.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (neg.f32 (.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
	95.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
	54.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))))

Compiler

Compiled 2 953 to 1 838 computations (37.8% saved)

series51.0ms (0.9%)

Memory

16.9MiB live, 110.1MiB allocated; 6ms collecting garbage

Counts

47 → 238

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	cosTheta	@	0	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) c) (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c)) (/ 1 c) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c) (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) (* (+ (/ -1 (sqrt (PI))) 1) (PI)) (+ (/ -1 (sqrt (PI))) 1))
8.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) c) (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c)) (/ 1 c) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c) (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) (* (+ (/ -1 (sqrt (PI))) 1) (PI)) (+ (/ -1 (sqrt (PI))) 1))
8.0ms	cosTheta	@	inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) c) (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c)) (/ 1 c) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c) (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) (* (+ (/ -1 (sqrt (PI))) 1) (PI)) (+ (/ -1 (sqrt (PI))) 1))
6.0ms	c	@	-inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) c) (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c)) (/ 1 c) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c) (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) (* (+ (/ -1 (sqrt (PI))) 1) (PI)) (+ (/ -1 (sqrt (PI))) 1))
4.0ms	c	@	0	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) c) (+ (* (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c)) (/ 1 c) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c) (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) (* (+ (/ -1 (sqrt (PI))) 1) (PI)) (+ (/ -1 (sqrt (PI))) 1))

rewrite718.0ms (13%)

Memory

-82.8MiB live, 349.4MiB allocated; 1.1s collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	994	13224
0	1067	11539
1	5828	11363
0	8088	11015

Stop Event

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

Counts

285 → 481

Calls

Call 1

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

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

eval70.0ms (1.3%)

Memory: -17.0MiB live, 124.8MiB allocated; 15ms collecting garbage
Compiler: Compiled 33 820 to 3 169 computations (90.6% saved)

prune36.0ms (0.7%)

Memory

-11.6MiB live, 81.6MiB allocated; 4ms collecting garbage

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	610	14	624
Fresh	11	12	23
Picked	3	2	5
Done	0	1	1
Total	624	29	653

Accuracy

100.0%

Counts

653 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	97.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	96.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
▶	96.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
	95.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx ( 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
▶	93.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx ( 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
	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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	95.3%	(/.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)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(approx (+ (* (neg cosTheta) cosTheta) 1) #s(literal 1 binary32))))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	92.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
✓	5.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (.f32 (*.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
	96.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32) (neg.f32 (.f32 (pow.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
✓	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 #s(approx (+ (/ -1 (sqrt (PI))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 #s(approx (+ (/ -1 (sqrt (PI))) c) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
▶	93.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 #s(approx (+ (+ (/ -1 (sqrt (PI))) c) 1) c) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
✓	93.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	95.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 #s(approx (+ ( (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (*.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)))) c)) cosTheta))
	95.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (.f32 cosTheta (/.f32 (fma.f32 (.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) c))) c)))
	95.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
▶	54.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))))

Compiler

Compiled 2 450 to 1 602 computations (34.6% saved)

series40.0ms (0.7%)

Memory

20.3MiB live, 66.7MiB allocated; 2ms collecting garbage

Counts

49 → 327

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	cosTheta	@	-inf	((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (* (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (* cosTheta cosTheta)) (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (* (/ 1 cosTheta) (sqrt (PI))) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
6.0ms	c	@	-inf	((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (* (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (* cosTheta cosTheta)) (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (* (/ 1 cosTheta) (sqrt (PI))) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
5.0ms	cosTheta	@	inf	((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (* (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (* cosTheta cosTheta)) (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (* (/ 1 cosTheta) (sqrt (PI))) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
3.0ms	cosTheta	@	0	((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (* (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (* cosTheta cosTheta)) (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (* (/ 1 cosTheta) (sqrt (PI))) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
3.0ms	c	@	0	((/ 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (PI))) (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (sqrt (+ (* cosTheta -2) 1)) (+ (* cosTheta -2) 1) cosTheta -2 (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (+ (* (- (* (* cosTheta cosTheta) 1/2) 1) (* cosTheta cosTheta)) 1) (- (* (* cosTheta cosTheta) 1/2) 1) (* (* cosTheta cosTheta) 1/2) (* cosTheta cosTheta) 1/2 (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ 1 cosTheta) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (* (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (* cosTheta cosTheta)) (+ (* (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -1 (* (/ 1 cosTheta) (sqrt (PI))) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))

rewrite257.0ms (4.6%)

Memory

22.4MiB live, 304.9MiB allocated; 78ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1121	20981
0	1194	18275
1	6248	17960
0	8349	17334

Stop Event

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

Counts

376 → 557

Calls

Call 1

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

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

eval64.0ms (1.2%)

Memory: -27.2MiB live, 112.8MiB allocated; 15ms collecting garbage
Compiler: Compiled 30 594 to 2 599 computations (91.5% saved)

prune45.0ms (0.8%)

Memory

8.2MiB live, 100.7MiB allocated; 4ms collecting garbage

Pruning

32 alts after pruning (28 fresh and 4 done)

	Pruned	Kept	Total
New	578	12	590
Fresh	5	16	21
Picked	4	1	5
Done	0	3	3
Total	587	32	619

Accuracy

100.0%

Counts

619 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	97.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) #s(approx (+ 1 c) #s(literal 1 binary32))))
	97.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	97.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	93.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
	96.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (-.f32 (.f32 #s(literal 1/2 binary32) cosTheta) #s(literal 3/2 binary32)) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	96.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	95.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (+ (* cosTheta -2) 1)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)))))
	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)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	97.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	92.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (+ (* (+ (* (/ 1 (sqrt (PI))) -3/2) (* (* 1/2 (/ 1 (sqrt (PI)))) cosTheta)) cosTheta) (neg (/ 1 (sqrt (PI))))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
✓	5.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (.f32 (.f32 (*.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta)) cosTheta)))
	96.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) (PI.f32) (neg.f32 (.f32 (pow.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))))) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
✓	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 #s(approx (+ (/ -1 (sqrt (PI))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (+.f32 #s(approx (+ (/ -1 (sqrt (PI))) c) c) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
✓	93.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 #s(approx (+ (+ (/ -1 (sqrt (PI))) c) 1) c) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	93.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (PI.f32)) cosTheta))
✓	93.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
	95.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) cosTheta)) cosTheta))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 #s(approx (+ ( (neg cosTheta) (PI)) (+ (* (/ 1 c) (sqrt (PI))) (/ (* (neg cosTheta) (* (+ (/ -1 (sqrt (PI))) 1) (PI))) c))) (*.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32)))) c)) cosTheta))
	95.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (* (+ (+ (/ -1 (sqrt (PI))) c) 1) (PI)) (neg cosTheta)) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (.f32 cosTheta (/.f32 (fma.f32 (.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32) #s(literal 1 binary32)) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) c))) c)))
	95.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (PI.f32) (/.f32 (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
	54.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) (*.f32 cosTheta cosTheta))))
	54.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (+.f32 #s(approx (+ (/ -1 (sqrt (PI))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))))
	51.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 #s(approx (+ ( (neg (PI)) (+ (+ (/ -1 (sqrt (PI))) c) 1)) (* (/ 1 cosTheta) (sqrt (PI)))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))) (.f32 cosTheta cosTheta))))

Compiler

Compiled 4 591 to 1 422 computations (69% saved)

regimes122.0ms (2.2%)

Memory

-7.1MiB live, 181.8MiB allocated; 12ms collecting garbage

Counts

68 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

18.0ms	(/.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)))))
17.0ms	cosTheta
16.0ms	c
16.0ms	(+.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))))
16.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes117.0ms (2.1%)

Memory

22.4MiB live, 115.6MiB allocated; 9ms collecting garbage

Counts

63 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

37.0ms	(.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)))
21.0ms	(/.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)))))
15.0ms	c
15.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
14.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes135.0ms (2.4%)

Memory

14.0MiB live, 105.2MiB allocated; 6ms collecting garbage

Counts

61 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

53.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
25.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
15.0ms	c
14.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
14.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes105.0ms (1.9%)

Memory

3.0MiB live, 98.7MiB allocated; 23ms collecting garbage

Counts

49 → 1

Calls

Call 1

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

Calls

6 calls:

32.0ms	(+.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)))))
12.0ms	c
12.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
11.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes74.0ms (1.3%)

Memory

1.3MiB live, 139.4MiB allocated; 10ms collecting garbage

Counts

48 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes79.0ms (1.4%)

Memory

-2.8MiB live, 133.8MiB allocated; 23ms collecting garbage

Counts

45 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

16.0ms	c
15.0ms	(/.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)))))
13.0ms	(+.f32 #s(literal 1 binary32) c)
11.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
11.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes72.0ms (1.3%)

Memory

-5.1MiB live, 141.3MiB allocated; 17ms collecting garbage

Counts

42 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

14.0ms	cosTheta
12.0ms	(+.f32 #s(literal 1 binary32) c)
12.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	c

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes62.0ms (1.1%)

Memory

32.6MiB live, 126.0MiB allocated; 4ms collecting garbage

Counts

41 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
97.3%	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)))`
97.3%	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))))`
97.3%	1	`(+.f32 #s(literal 1 binary32) c)`
97.3%	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)))))`
97.3%	1	`cosTheta`
97.3%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes55.0ms (1%)

Memory

-30.6MiB live, 113.4MiB allocated; 7ms collecting garbage

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes42.0ms (0.8%)

Memory

34.8MiB live, 80.9MiB allocated; 7ms collecting garbage

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

10.0ms	cosTheta
6.0ms	c
6.0ms	(/.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)))))
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
6.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
96.1%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.1%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.1%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.1%	1	`cosTheta`
96.1%	1	`(+.f32 #s(literal 1 binary32) c)`
96.1%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes53.0ms (1%)

Memory

-41.0MiB live, 61.3MiB allocated; 14ms collecting garbage

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

17.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
6.0ms	c
6.0ms	(+.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))))
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.0%	1	`(+.f32 #s(literal 1 binary32) c)`
96.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.0%	1	`cosTheta`
96.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.0%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes35.0ms (0.6%)

Memory

12.7MiB live, 59.7MiB allocated; 2ms collecting garbage

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
96.0%	1	`(+.f32 #s(literal 1 binary32) c)`
96.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.0%	1	`cosTheta`
96.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.0%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes28.0ms (0.5%)

Memory

14.7MiB live, 59.5MiB allocated; 4ms collecting garbage

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

7.0ms	(/.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)))))
4.0ms	(+.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))))
4.0ms	c
4.0ms	(.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)))
4.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.0%	1	`(+.f32 #s(literal 1 binary32) c)`
96.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.0%	1	`cosTheta`
96.0%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes22.0ms (0.4%)

Memory

-0.3MiB live, 49.3MiB allocated; 5ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

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

Calls

6 calls:

6.0ms	cosTheta
3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
3.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	c

Results

Accuracy	Segments	Branch
93.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
93.7%	1	`(+.f32 #s(literal 1 binary32) c)`
93.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
93.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
93.7%	1	`cosTheta`
93.7%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes8.0ms (0.1%)

Memory

-27.2MiB live, 19.3MiB allocated; 3ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

3.0ms	c
1.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
1.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
1.0ms	cosTheta

Results

Accuracy	Segments	Branch
5.3%	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)))))`
5.3%	1	`cosTheta`
5.3%	1	`c`
5.3%	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)))`
5.3%	1	`(+.f32 #s(literal 1 binary32) c)`
5.3%	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))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify74.0ms (1.3%)

Memory

35.7MiB live, 81.8MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	505
1	161	493
2	321	488
3	1024	487
4	4864	487

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations323.0ms (5.8%)

Memory

3.4MiB live, 378.3MiB allocated; 37ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 505 to 112 computations (77.8% saved)

preprocess64.0ms (1.2%)

Memory: -23.1MiB live, 119.9MiB allocated; 26ms collecting garbage
Compiler: Compiled 1 060 to 260 computations (75.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze35.0ms (0.6%)

sample1.6s (29.4%)

explain262.0ms (4.7%)

preprocess181.0ms (3.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series48.0ms (0.9%)

rewrite157.0ms (2.8%)

eval27.0ms (0.5%)

prune17.0ms (0.3%)

series54.0ms (1%)

rewrite263.0ms (4.8%)

eval74.0ms (1.3%)

prune37.0ms (0.7%)

series51.0ms (0.9%)

rewrite718.0ms (13%)

eval70.0ms (1.3%)

prune36.0ms (0.7%)

series40.0ms (0.7%)

rewrite257.0ms (4.6%)

eval64.0ms (1.2%)

prune45.0ms (0.8%)

regimes122.0ms (2.2%)

regimes117.0ms (2.1%)

regimes135.0ms (2.4%)

regimes105.0ms (1.9%)

regimes74.0ms (1.3%)

regimes79.0ms (1.4%)

regimes72.0ms (1.3%)

regimes62.0ms (1.1%)

regimes55.0ms (1%)

regimes42.0ms (0.8%)

regimes53.0ms (1%)

regimes35.0ms (0.6%)

regimes28.0ms (0.5%)

regimes22.0ms (0.4%)

regimes8.0ms (0.1%)

simplify74.0ms (1.3%)

derivations323.0ms (5.8%)

preprocess64.0ms (1.2%)

end0.0ms (0%)

Profiling