Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

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

analyze17.0ms (0.5%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms 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)

sample985.0ms (26.5%)

Memory

-13.0MiB live, 1 447.1MiB allocated; 190ms collecting garbage

Samples

708.0ms	8 255×	0	valid
5.0ms	53×	0	invalid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 520.0ms

ival-mult!: 107.0ms (20.6% of total)

ival-exp: 104.0ms (20% of total)

ival-div!: 96.0ms (18.4% of total)

ival-sqrt: 79.0ms (15.2% of total)

ival-sub!: 53.0ms (10.2% of total)

ival-add!: 44.0ms (8.5% of total)

ival-neg: 37.0ms (7.1% of total)

adjust: 2.0ms (0.4% of total)

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

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

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

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

Bogosity

explain206.0ms (5.5%)

Memory

-1.4MiB live, 355.6MiB allocated; 65ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f32`	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms

512×

valid

Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions

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

ival-mult!: 6.0ms (21.4% of total)

ival-div!: 5.0ms (17.9% of total)

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

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

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

ival-add!: 3.0ms (10.7% of total)

ival-sub!: 2.0ms (7.1% of total)

adjust: 0.0ms (0% of total)

preprocess28.0ms (0.7%)

Memory

-20.5MiB live, 26.8MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	158
1	144	142
2	491	134
3	2194	132

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Accuracy

Program

▶

97.9%

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

Compiler

Compiled 50 to 36 computations (28% saved)

series39.0ms (1%)

Memory

15.4MiB live, 64.4MiB allocated; 6ms 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
11.0ms	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))
9.0ms	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))
8.0ms	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))
4.0ms	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))
2.0ms	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))

rewrite151.0ms (4.1%)

Memory

-16.5MiB live, 220.7MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	634	6295
0	658	5601
0	3784	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)))))))))
#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)))))

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

eval22.0ms (0.6%)

Memory: 2.4MiB live, 49.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 8 352 to 1 156 computations (86.2% saved)

prune12.0ms (0.3%)

Memory

29.8MiB live, 29.8MiB allocated; 0ms collecting garbage

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	147	17	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	17	165

Accuracy

99.4%

Counts

165 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
	95.5%	(/.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)))))
▶	96.5%	(/.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))))
	95.5%	(/.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))))
	92.7%	(/.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)))))))
	97.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #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)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	97.1%	(/.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 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	95.4%	(/.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 (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)))
	97.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) c))))
	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))))))
	52.4%	(/.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) (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
	53.1%	(/.f32 #s(literal 1 binary32) #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 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c))))
▶	5.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
▶	96.1%	#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 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) 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 (sqrt.f32 (PI.f32)) cosTheta))

Compiler

Compiled 1 244 to 860 computations (30.9% saved)

series42.0ms (1.1%)

Memory

-20.7MiB live, 77.2MiB allocated; 11ms collecting garbage

Counts

43 → 238

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta	@	0	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (neg (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 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 c) (* (* (/ 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) (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))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (* (/ 1 (sqrt (PI))) -3/2) -3/2)
6.0ms	cosTheta	@	-inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (neg (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 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 c) (* (* (/ 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) (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))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (* (/ 1 (sqrt (PI))) -3/2) -3/2)
5.0ms	cosTheta	@	inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (neg (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 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 c) (* (* (/ 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) (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))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (* (/ 1 (sqrt (PI))) -3/2) -3/2)
3.0ms	c	@	-inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (neg (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 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 c) (* (* (/ 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) (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))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (* (/ 1 (sqrt (PI))) -3/2) -3/2)
3.0ms	c	@	0	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (neg (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 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 c) (* (* (/ 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) (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))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (* (/ 1 (sqrt (PI))) -3/2) -3/2)

rewrite198.0ms (5.3%)

Memory

-6.4MiB live, 230.4MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	921	13318
0	990	11368
0	5130	10866

Stop Event

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

Counts

281 → 460

Calls

Call 1

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

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

eval56.0ms (1.5%)

Memory: 43.1MiB live, 90.0MiB allocated; 3ms collecting garbage
Compiler: Compiled 20 448 to 2 442 computations (88.1% saved)

prune33.0ms (0.9%)

Memory

-0.9MiB live, 46.0MiB allocated; 5ms collecting garbage

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	383	22	405
Fresh	8	4	12
Picked	4	1	5
Done	0	0	0
Total	395	27	422

Accuracy

99.6%

Counts

422 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
▶	96.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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))))
▶	98.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
▶	97.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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 c #s(literal 1 binary32))))
	95.5%	(/.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))))))
	95.5%	(/.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 #s(approx (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	92.8%	(/.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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	97.1%	(/.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 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	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))))))
	52.4%	(/.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) (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
✓	5.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	95.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/.f32 (fma.f32 (+.f32 (+.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)))
	96.1%	#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)))
	96.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (.f32 (*.f32 (PI.f32) cosTheta) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) #s(literal -1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
▶	96.1%	#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 (+ (neg (/ 1 (sqrt (PI)))) c) (-.f32 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 (+ (neg (/ 1 (sqrt (PI)))) c) c) #s(literal 1 binary32)) (PI.f32)) (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 #s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (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 (sqrt.f32 (PI.f32)) cosTheta))
	95.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 (.f32 (*.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (neg.f32 (.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
	57.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) (*.f32 cosTheta cosTheta))))

Compiler

Compiled 2 351 to 1 510 computations (35.8% saved)

series38.0ms (1%)

Memory

-32.9MiB live, 65.2MiB allocated; 8ms collecting garbage

Counts

36 → 282

Calls

Call 1

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

Outputs
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (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 (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (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)))))))))))))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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)))))))))))))
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#s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) #s(hole binary32 (* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))))
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#s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (- c (/ 1 (sqrt (PI)))) #s(hole binary32 c))
#s(approx (- c (/ 1 (sqrt (PI)))) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #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 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #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 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) 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 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) 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)))))
#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 (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))))) c)) (* (pow cosTheta 2) (PI)))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))) c)) (* cosTheta (PI)))))))
#s(approx (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (- 1 (sqrt (/ 1 (PI))))) c)))))))
#s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) #s(hole binary32 (* -1 (* c (- (* -1 (/ (- 1 (sqrt (/ 1 (PI)))) c)) 1)))))
#s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (- c (/ 1 (sqrt (PI)))) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) 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 (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) 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)))))
#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #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 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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 (- (- 1 cosTheta) cosTheta)) 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	@	0	((/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (- c (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
6.0ms	cosTheta	@	-inf	((/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (- c (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
5.0ms	cosTheta	@	inf	((/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (- c (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
2.0ms	c	@	-inf	((/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (- c (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))
2.0ms	c	@	inf	((/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 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))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (+ (neg (/ 1 (sqrt (PI)))) c) (- c (/ 1 (sqrt (PI)))) (/ 1 (sqrt (PI))) (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (exp (* (neg cosTheta) cosTheta)) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)) (+ (* (neg cosTheta) cosTheta) 1))

rewrite202.0ms (5.4%)

Memory

31.2MiB live, 311.7MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	958	18847
0	1018	16307
0	5137	15536

Stop Event

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

Counts

318 → 428

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
#s(literal 1 binary32)
(fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) 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
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(sqrt.f32 (PI.f32))
(PI.f32)
(exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))
(*.f32 (neg.f32 cosTheta) cosTheta)
(neg.f32 cosTheta)
(+.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 (sqrt.f32 (PI.f32)) cosTheta))
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#s(approx (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) #s(hole binary32 (+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 c))
#s(approx (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 (* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))))
#s(approx (+ c 1) #s(hole binary32 c))
#s(approx (+ c 1) #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 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 (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* -1 (* c (* (pow cosTheta 2) (PI))))))
#s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) #s(hole binary32 (* c (+ (* -1 (* (pow cosTheta 2) (PI))) (/ (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI))))))))) c)))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (* cosTheta (PI))))))
#s(approx (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* c (+ (* -1 (* cosTheta (PI))) (+ (* -1 (/ (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))) c)) (* (/ 1 c) (sqrt (PI))))))))
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#s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) #s(hole binary32 c))
#s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) #s(hole binary32 (* c (- (+ 1 (/ 1 c)) (* (/ 1 c) (sqrt (/ 1 (PI))))))))
#s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(hole binary32 c))
#s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (- c (/ 1 (sqrt (PI)))) #s(hole binary32 c))
#s(approx (- c (/ 1 (sqrt (PI)))) #s(hole binary32 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ 1 c)))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) #s(hole binary32 c))
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#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #s(hole binary32 (/ 1 c)))
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#s(approx (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #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 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) #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 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) #s(hole binary32 c))
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#s(approx (/ 1 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #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 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) 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 (+ (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* (sqrt (PI)) 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)))))
#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))))
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#s(approx (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) #s(hole binary32 (* -1 (* c (+ (* -1 (/ (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (- 1 (sqrt (/ 1 (PI)))))))) c)) (* cosTheta (PI)))))))
#s(approx (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) #s(hole binary32 (* -1 (* c (+ (* -1 (PI)) (* -1 (/ (* (PI) (- 1 (sqrt (/ 1 (PI))))) c)))))))
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#s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (- c (/ 1 (sqrt (PI)))) #s(hole binary32 (* -1 (* c (- (* (/ 1 c) (sqrt (/ 1 (PI)))) 1)))))
#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) #s(hole binary32 (* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))))
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#s(approx (/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) 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))))
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Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (fma.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (+.f32 c #s(literal 1 binary32))) #s(literal -1 binary32))
#s(literal 1 binary32)
(/.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 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)) (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta)))) (-.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta))))
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c
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eval50.0ms (1.3%)

Memory: 2.5MiB live, 101.2MiB allocated; 17ms collecting garbage
Compiler: Compiled 17 207 to 1 973 computations (88.5% saved)

prune28.0ms (0.8%)

Memory

3.4MiB live, 50.5MiB allocated; 3ms collecting garbage

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	360	13	373
Fresh	5	16	21
Picked	2	3	5
Done	0	1	1
Total	367	33	400

Accuracy

99.6%

Counts

400 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))))
▶	98.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	96.2%	(/.f32 #s(literal 1 binary32) (fma.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 c #s(literal 1 binary32))))
✓	96.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
	96.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) #s(approx (+ c 1) #s(literal 1 binary32))))
	93.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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))))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
✓	98.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
	96.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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)))) #s(approx (+ c 1) #s(literal 1 binary32))))
	95.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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 c #s(literal 1 binary32))))
▶	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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))))
▶	96.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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))))
▶	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	92.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	95.5%	(/.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))))))
	92.8%	(/.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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	97.1%	(/.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 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	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))))))
	52.4%	(/.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) (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
✓	5.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	96.1%	#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)))
	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 (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (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 #s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (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 (sqrt.f32 (PI.f32)) cosTheta))
	95.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 (.f32 (*.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (neg.f32 (.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
	57.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) (*.f32 cosTheta cosTheta))))

Compiler

Compiled 2 471 to 1 604 computations (35.1% saved)

series39.0ms (1%)

Memory

-21.9MiB live, 75.4MiB allocated; 8ms collecting garbage

Counts

47 → 279

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta	@	-inf	((/ 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (neg cosTheta) 1) cosTheta) (+ (neg cosTheta) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) (- (* -3/2 cosTheta) 1) (* -3/2 cosTheta) -3/2 (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (* (- (* 1/2 cosTheta) 3/2) cosTheta) (- (* 1/2 cosTheta) 3/2) (* 1/2 cosTheta) 1/2 3/2)
6.0ms	cosTheta	@	inf	((/ 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (neg cosTheta) 1) cosTheta) (+ (neg cosTheta) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) (- (* -3/2 cosTheta) 1) (* -3/2 cosTheta) -3/2 (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (* (- (* 1/2 cosTheta) 3/2) cosTheta) (- (* 1/2 cosTheta) 3/2) (* 1/2 cosTheta) 1/2 3/2)
6.0ms	cosTheta	@	0	((/ 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (neg cosTheta) 1) cosTheta) (+ (neg cosTheta) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) (- (* -3/2 cosTheta) 1) (* -3/2 cosTheta) -3/2 (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (* (- (* 1/2 cosTheta) 3/2) cosTheta) (- (* 1/2 cosTheta) 3/2) (* 1/2 cosTheta) 1/2 3/2)
5.0ms	c	@	-inf	((/ 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (neg cosTheta) 1) cosTheta) (+ (neg cosTheta) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) (- (* -3/2 cosTheta) 1) (* -3/2 cosTheta) -3/2 (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (* (- (* 1/2 cosTheta) 3/2) cosTheta) (- (* 1/2 cosTheta) 3/2) (* 1/2 cosTheta) 1/2 3/2)
2.0ms	c	@	0	((/ 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (+ c 1) c (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI)) (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (neg cosTheta) 1) cosTheta) (+ (neg cosTheta) 1) (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) (- (* -3/2 cosTheta) 1) (* -3/2 cosTheta) -3/2 (/ 1 (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1))) (+ (* (/ 1 (sqrt (PI))) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ c 1)) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) cosTheta) (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) (* (- (* 1/2 cosTheta) 3/2) cosTheta) (- (* 1/2 cosTheta) 3/2) (* 1/2 cosTheta) 1/2 3/2)

rewrite201.0ms (5.4%)

Memory

15.6MiB live, 297.7MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1008	15669
0	1079	13772
0	5453	13179

Stop Event

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

Counts

326 → 461

Calls

Call 1

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

eval52.0ms (1.4%)

Memory: -30.7MiB live, 114.7MiB allocated; 12ms collecting garbage
Compiler: Compiled 18 750 to 2 271 computations (87.9% saved)

prune36.0ms (1%)

Memory

39.3MiB live, 86.8MiB allocated; 2ms collecting garbage

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	379	10	389
Fresh	3	21	24
Picked	3	2	5
Done	1	3	4
Total	386	36	422

Accuracy

99.7%

Counts

422 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))))
	97.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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))))
	95.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32))) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
	96.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) #s(approx (+ c 1) #s(literal 1 binary32))))
	93.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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))))
	95.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
✓	98.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.9%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
	96.6%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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)))) #s(approx (+ c 1) #s(literal 1 binary32))))
✓	97.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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))))
	96.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
	96.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
	92.7%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	46.8%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) (.f32 (-.f32 (neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) #s(literal 3/2 binary32)) (.f32 cosTheta cosTheta))) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	53.0%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))) (+.f32 c #s(literal 1 binary32))))
	95.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (neg cosTheta) 1) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))
	96.4%	(/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) c) #s(literal 1 binary32)))
	95.5%	(/.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))))))
	92.8%	(/.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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	97.1%	(/.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 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	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))))))
	52.4%	(/.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) (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
✓	5.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) c))
	96.1%	#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)))
	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 (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (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 #s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (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 (sqrt.f32 (PI.f32)) cosTheta))
	95.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 (.f32 (*.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (neg.f32 (.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
	57.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) (*.f32 cosTheta cosTheta))))

Compiler

Compiled 3 912 to 1 326 computations (66.1% saved)

regimes106.0ms (2.8%)

Memory

-22.0MiB live, 218.1MiB allocated; 19ms 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))
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(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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)))) (neg.f32 (.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c))))
(/.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) (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))

Outputs

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

Calls

6 calls:

19.0ms	cosTheta
18.0ms	c
17.0ms	(.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)))
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)))))
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))))

Results

Accuracy	Segments	Branch
98.7%	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)))`
98.7%	1	`(+.f32 #s(literal 1 binary32) c)`
98.7%	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))))`
98.7%	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)))))`
98.7%	1	`cosTheta`
98.7%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes88.0ms (2.4%)

Memory

0.8MiB live, 191.9MiB allocated; 11ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

16.0ms	c
15.0ms	(.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)))
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))))
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	cosTheta

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 #s(literal 1 binary32) c)`
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)

regimes86.0ms (2.3%)

Memory

-12.4MiB live, 179.5MiB allocated; 10ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

15.0ms	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)))))
15.0ms	(.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	cosTheta
13.0ms	(+.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
97.9%	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)))`
97.9%	1	`(+.f32 #s(literal 1 binary32) c)`
97.9%	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))))`
97.9%	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)))))`
97.9%	1	`cosTheta`
97.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes79.0ms (2.1%)

Memory

25.5MiB live, 170.5MiB allocated; 7ms 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.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 (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) 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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.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) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
#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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (neg cosTheta) 1) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 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))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) (-.f32 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 (neg.f32 cosTheta) (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(approx (exp (* (neg 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 (fma.f32 (.f32 (*.f32 (PI.f32) cosTheta) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) #s(literal -1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) #s(approx (+ c 1) #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 (.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 (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/.f32 (fma.f32 (+.f32 (+.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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(approx (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (/.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (+.f32 (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) (+.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) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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 (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 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) c) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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))) (.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)))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))) (+.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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (neg.f32 (.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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 (.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) (fma.f32 (neg.f32 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) 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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta) c)) c)))
(/.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 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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:

14.0ms	(+.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
13.0ms	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)))
12.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes77.0ms (2.1%)

Memory

4.2MiB live, 148.7MiB allocated; 23ms 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.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 (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) 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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.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) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
#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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (neg cosTheta) 1) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 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))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) (-.f32 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 (neg.f32 cosTheta) (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(approx (exp (* (neg 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 (fma.f32 (.f32 (*.f32 (PI.f32) cosTheta) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) #s(literal -1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) #s(approx (+ c 1) #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 (.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 (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/.f32 (fma.f32 (+.f32 (+.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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(approx (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (/.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (+.f32 (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) (+.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) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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 (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 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) c) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (.f32 (fma.f32 (neg.f32 (PI.f32)) (-.f32 (+.f32 c #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta)) cosTheta)) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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))) (.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)))) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* -3/2 cosTheta) 1) cosTheta) 1) cosTheta) (.f32 (-.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3/2 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)) cosTheta))) (+.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) (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (PI))) (sqrt (PI))) (neg.f32 (.f32 (fma.f32 (PI.f32) cosTheta (neg.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32)) (sqrt.f32 (PI.f32))) c))) c))) cosTheta))

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (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:

20.0ms	(/.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	c
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)))
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	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes62.0ms (1.7%)

Memory

-14.6MiB live, 129.7MiB allocated; 8ms collecting garbage

Counts

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

Outputs

(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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:

12.0ms	c
11.0ms	(/.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)))
9.0ms	(+.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))))
9.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes59.0ms (1.6%)

Memory

-17.3MiB live, 124.7MiB 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.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 (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) 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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.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) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
#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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (neg cosTheta) 1) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 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))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) (-.f32 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 (neg.f32 cosTheta) (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(approx (exp (* (neg 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 (fma.f32 (.f32 (*.f32 (PI.f32) cosTheta) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) #s(literal -1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) #s(approx (+ c 1) #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 (.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 (- (- 1 cosTheta) cosTheta)) 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)) #s(approx (+ c 1) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (sqrt (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/.f32 (fma.f32 (+.f32 (+.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) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 #s(approx (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) (/.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) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (+.f32 (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) (+.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) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.f32 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.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 c #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) 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 (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 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) 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)) c) #s(literal 1 binary32)))

Outputs

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

Calls

6 calls:

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
9.0ms	(/.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)))))
9.0ms	c
9.0ms	(.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
96.4%	1	`(+.f32 #s(literal 1 binary32) c)`
96.4%	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)))`
96.4%	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))))`
96.4%	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)))))`
96.4%	1	`cosTheta`
96.4%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes55.0ms (1.5%)

Memory

26.7MiB live, 124.0MiB allocated; 5ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

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
9.0ms	(.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)))
9.0ms	(/.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	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes47.0ms (1.3%)

Memory

11.6MiB live, 106.8MiB allocated; 4ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes40.0ms (1.1%)

Memory

-8.7MiB live, 88.0MiB allocated; 5ms collecting garbage

Counts

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

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	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	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)))))

Results

Accuracy	Segments	Branch
96.1%	1	`(+.f32 #s(literal 1 binary32) c)`
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	`c`
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))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes38.0ms (1%)

Memory

-16.0MiB live, 78.9MiB allocated; 4ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

7.0ms	c
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 #s(literal 1 binary32) c)
6.0ms	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 #s(literal 1 binary32) c)`
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	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes34.0ms (0.9%)

Memory

26.5MiB live, 76.2MiB allocated; 3ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

7.0ms	c
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	cosTheta

Results

Accuracy	Segments	Branch
96.1%	1	`(+.f32 #s(literal 1 binary32) c)`
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	`c`
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))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes34.0ms (0.9%)

Memory

-20.6MiB live, 74.8MiB allocated; 4ms 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.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 (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) 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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.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) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
#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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (neg cosTheta) 1) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 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))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) (-.f32 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 (neg.f32 cosTheta) (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) #s(approx (exp (* (neg cosTheta) cosTheta)) #s(literal 1 binary32)) (+.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 (neg.f32 cosTheta) (*.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) (-.f32 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	c
7.0ms	(+.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	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)))))

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 #s(literal 1 binary32) c)`
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	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes28.0ms (0.8%)

Memory

16.2MiB live, 64.0MiB allocated; 2ms 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.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 (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) 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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.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) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) #s(approx (+ c 1) #s(literal 1 binary32))))
#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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) #s(approx ( 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (neg cosTheta) 1) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) 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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (+.f32 (neg.f32 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 (neg.f32 cosTheta) (*.f32 #s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))

Calls

6 calls:

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))))
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	(/.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	c
4.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes23.0ms (0.6%)

Memory

4.9MiB live, 53.6MiB allocated; 3ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

5.0ms	c
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))))
3.0ms	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)))))

Results

Accuracy	Segments	Branch
95.3%	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)))`
95.3%	1	`(+.f32 #s(literal 1 binary32) c)`
95.3%	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))))`
95.3%	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)))))`
95.3%	1	`cosTheta`
95.3%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes23.0ms (0.6%)

Memory

-44.7MiB live, 50.4MiB allocated; 4ms 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 (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) c) (PI.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)))) (*.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 (+ (neg (/ 1 (sqrt (PI)))) 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 (neg.f32 cosTheta) (.f32 (+.f32 #s(approx (+ (neg (/ 1 (sqrt (PI)))) c) #s(approx (- c (/ 1 (sqrt (PI)))) c)) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) 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 #s(approx (+ (* (+ (* (* (/ 1 (sqrt (PI))) -3/2) cosTheta) (neg (/ 1 (sqrt (PI))))) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(literal 1 binary32) cosTheta)) (+.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 (- (- 1 cosTheta) cosTheta)) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 #s(approx (+ (* (- (* (- (* 1/2 cosTheta) 3/2) cosTheta) 1) cosTheta) 1) #s(literal 1 binary32)) cosTheta)) (+.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)))))))

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:

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))))
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	cosTheta
3.0ms	c

Results

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

regimes7.0ms (0.2%)

Memory

21.1MiB live, 21.1MiB allocated; 0ms 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:

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	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 (/.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
5.0%	1	`(+.f32 #s(literal 1 binary32) c)`
5.0%	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)))))`
5.0%	1	`cosTheta`
5.0%	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)))`
5.0%	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))))`
5.0%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

derivations272.0ms (7.3%)

Memory

2.6MiB live, 386.9MiB allocated; 18ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 566 to 110 computations (80.6% saved)

preprocess125.0ms (3.4%)

Memory: 22.5MiB live, 341.1MiB allocated; 33ms collecting garbage
Compiler: Compiled 1 182 to 256 computations (78.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze17.0ms (0.5%)

sample985.0ms (26.5%)

explain206.0ms (5.5%)

preprocess28.0ms (0.7%)

series39.0ms (1%)

rewrite151.0ms (4.1%)

eval22.0ms (0.6%)

prune12.0ms (0.3%)

series42.0ms (1.1%)

rewrite198.0ms (5.3%)

eval56.0ms (1.5%)

prune33.0ms (0.9%)

series38.0ms (1%)

rewrite202.0ms (5.4%)

eval50.0ms (1.3%)

prune28.0ms (0.8%)

series39.0ms (1%)

rewrite201.0ms (5.4%)

eval52.0ms (1.4%)

prune36.0ms (1%)

regimes106.0ms (2.8%)

regimes88.0ms (2.4%)

regimes86.0ms (2.3%)

regimes79.0ms (2.1%)

regimes77.0ms (2.1%)

regimes62.0ms (1.7%)

regimes59.0ms (1.6%)

regimes55.0ms (1.5%)

regimes47.0ms (1.3%)

regimes40.0ms (1.1%)

regimes38.0ms (1%)

regimes34.0ms (0.9%)

regimes34.0ms (0.9%)

regimes28.0ms (0.8%)

regimes23.0ms (0.6%)

regimes23.0ms (0.6%)

regimes7.0ms (0.2%)

derivations272.0ms (7.3%)

preprocess125.0ms (3.4%)

end0.0ms (0%)

Profiling