Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

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

analyze23.0ms (0.7%)

Memory

-5.2MiB live, 39.6MiB allocated; 10ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample1.1s (33.7%)

Memory

49.5MiB live, 2 046.9MiB allocated; 484ms collecting garbage

Samples

754.0ms	8 255×	0	valid
9.0ms	66×	0	invalid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 554.0ms

ival-mult!: 134.0ms (24.2% of total)

ival-div!: 110.0ms (19.8% of total)

ival-sqrt: 85.0ms (15.3% of total)

ival-exp: 71.0ms (12.8% of total)

ival-neg: 66.0ms (11.9% of total)

ival-add!: 50.0ms (9% of total)

ival-sub!: 36.0ms (6.5% 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

preprocess51.0ms (1.6%)

Memory

-38.1MiB live, 51.6MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	158
1	188	142
2	789	126
3	5216	126

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

97.8%

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

Compiler

Compiled 42 to 36 computations (14.3% saved)

series36.0ms (1.1%)

Memory

9.9MiB live, 62.5MiB allocated; 8ms collecting garbage

Counts

18 → 100

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 (/ (+ (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 (/ (+ (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 (* -2 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#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 (* 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 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 (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 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
10.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
8.0ms	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))
3.0ms	cosTheta	@	0	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
1.0ms	c	@	inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))

rewrite131.0ms (4%)

Memory

23.4MiB live, 160.5MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	623	6146
0	647	5455
0	3776	5150

Stop Event

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

Counts

118 → 166

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

eval21.0ms (0.6%)

Memory: -8.7MiB live, 42.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 4 260 to 1 080 computations (74.6% saved)

prune17.0ms (0.5%)

Memory

-9.8MiB live, 36.7MiB allocated; 2ms collecting garbage

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	132	19	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	19	152

Accuracy

99.3%

Counts

152 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(/.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))))
	97.8%	(/.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) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta))) (+.f32 c #s(literal 1 binary32))))
	54.6%	(/.f32 #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))))))
	33.5%	(/.f32 #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 (.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))))))))
	98.4%	(/.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)))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
	97.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
	97.4%	(/.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))))
▶	96.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (+.f32 (+.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)))
▶	97.8%	(/.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))))
	93.0%	(/.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))))))
▶	54.6%	(/.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)))
	97.8%	#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)))))
▶	5.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (-.f32 (.f32 (neg.f32 cosTheta) (+.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32) (neg.f32 (.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (neg.f32 (.f32 (.f32 (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #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)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) cosTheta) (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	97.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) (.f32 (+.f32 (+.f32 (neg.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	96.9%	#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))
	93.8%	#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 1 478 to 1 058 computations (28.4% saved)

series48.0ms (1.5%)

Memory

-2.1MiB live, 89.1MiB allocated; 6ms collecting garbage

Counts

41 → 183

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

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 (/ (+ (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 (- (- 1 cosTheta) cosTheta) #s(hole binary32 (+ 1 (* -2 cosTheta))))
#s(approx cosTheta #s(hole binary32 cosTheta))
#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 (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI)))))) cosTheta)))
#s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (sqrt (/ 1 (PI)))))
#s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (- (+ 1 c) (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (* -1 (sqrt (/ 1 (PI))))))) cosTheta)))
#s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)))
#s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 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 (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))))
#s(approx (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
#s(approx (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) #s(hole binary32 (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))))
#s(approx (/ (- (- 1 cosTheta) cosTheta) (PI)) #s(hole binary32 (/ 1 (PI))))
#s(approx (/ (- (- 1 cosTheta) cosTheta) (PI)) #s(hole binary32 (+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ 1 cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* -1 (pow cosTheta 2))) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* (pow cosTheta 2) (- (* 1/2 (pow cosTheta 2)) 1))) cosTheta)))
#s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) #s(hole binary32 (/ (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ 1/2 (* -1/6 (pow cosTheta 2)))) 1))) cosTheta)))
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#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 (+ c 1) #s(hole binary32 (* c (+ 1 (/ 1 c)))))
#s(approx (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* c (- (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 c))) (* (/ 1 c) (sqrt (/ 1 (PI))))))))
#s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (- 1 (sqrt (/ 1 (PI))))) 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 (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))
#s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* c (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))))
#s(approx (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) #s(hole binary32 (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 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 (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) #s(hole binary32 (* -1 (* c (- (* -1 (/ (- (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (sqrt (/ 1 (PI)))) c)) 1)))))
#s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) #s(hole binary32 (* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (- 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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 1)))))
#s(approx (* (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) c) #s(hole binary32 (* -1 (* c (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) (+ 1 (/ 1 c)))))))
#s(approx (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) #s(hole binary32 (+ 1 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 1) c)))))
#s(approx (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c)) #s(hole binary32 (* -1 (/ (- (* -1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 1) c))))

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	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 (+ (+ 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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (- (- 1 cosTheta) cosTheta) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) c) (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c))
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 (+ (+ 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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (- (- 1 cosTheta) cosTheta) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) c) (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c))
7.0ms	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 (+ (+ 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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (- (- 1 cosTheta) cosTheta) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) c) (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c))
5.0ms	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 (+ (+ 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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (- (- 1 cosTheta) cosTheta) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) c) (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c))
4.0ms	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 (+ (+ 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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (- (- 1 cosTheta) cosTheta) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) c) (+ 1 (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c))

rewrite337.0ms (10.3%)

Memory

30.7MiB live, 275.1MiB allocated; 59ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	976	10967
0	1048	9630
1	6034	9412
0	8202	8983

Stop Event

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

Counts

224 → 391

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

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

eval104.0ms (3.2%)

Memory: -29.9MiB live, 106.9MiB allocated; 13ms collecting garbage
Compiler: Compiled 10 817 to 2 889 computations (73.3% saved)

prune39.0ms (1.2%)

Memory

13.1MiB live, 62.0MiB allocated; 24ms collecting garbage

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	454	22	476
Fresh	11	3	14
Picked	4	1	5
Done	0	0	0
Total	469	26	495

Accuracy

99.8%

Counts

495 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.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))))
	98.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	98.2%	(/.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)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	98.0%	(/.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))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	93.5%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
▶	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1 binary32))))
	96.4%	(/.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) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)))) c) #s(literal 1 binary32)) cosTheta (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)))) cosTheta)))
▶	96.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	95.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (.f32 (+.f32 cosTheta (fma.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) c))) c)) cosTheta)))
	97.5%	(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c))))
	96.3%	(/.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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) c))))
	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 (exp.f32 (.f32 (log.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1/2 binary32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) c))))
	96.3%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))))
	97.4%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))))))
	93.0%	(/.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))))))
	53.1%	(/.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 #s(approx (/ (exp ( (neg cosTheta) cosTheta)) (* cosTheta c)) (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
	49.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 #s(approx (+ 1 (+ ( (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 c cosTheta)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) c)))
	90.3%	(exp.f32 (.f32 (log.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)))
✓	5.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (-.f32 (.f32 (neg.f32 cosTheta) (+.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32) (neg.f32 (.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (neg.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))))))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) cosTheta) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	97.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	96.9%	#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))
▶	93.8%	#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 1 765 to 1 459 computations (17.3% saved)

series48.0ms (1.4%)

Memory

21.9MiB live, 53.7MiB allocated; 23ms collecting garbage

Counts

41 → 129

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

Calls

6 calls:

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

rewrite210.0ms (6.4%)

Memory

0.3MiB live, 164.0MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	756	7341
0	813	6413
0	4626	6109

Stop Event

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

Counts

170 → 296

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

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

eval56.0ms (1.7%)

Memory: -6.3MiB live, 77.7MiB allocated; 12ms collecting garbage
Compiler: Compiled 6 657 to 1 777 computations (73.3% saved)

prune24.0ms (0.7%)

Memory

13.5MiB live, 58.8MiB allocated; 4ms collecting garbage

Pruning

26 alts after pruning (22 fresh and 4 done)

	Pruned	Kept	Total
New	307	5	312
Fresh	3	17	20
Picked	2	3	5
Done	0	1	1
Total	312	26	338

Accuracy

99.8%

Counts

338 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	98.0%	(/.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))))
	98.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	93.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
✓	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (fma.f32 (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
▶	97.5%	(/.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)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))
	97.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (/.f32 (-.f32 (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (.f32 (neg.f32 cosTheta) cosTheta)) #s(literal 1 binary32)) (-.f32 (.f32 (neg.f32 cosTheta) cosTheta) #s(literal 1 binary32)))))))
	46.5%	(/.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) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta)))))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1 binary32))))
▶	96.4%	(/.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) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)))) c) #s(literal 1 binary32)) cosTheta (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)))) cosTheta)))
✓	96.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
▶	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	95.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (.f32 (+.f32 cosTheta (fma.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta) c))) c)) cosTheta)))
	97.5%	(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c))))
	96.3%	(/.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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) c))))
▶	96.3%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))))
	97.4%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))))))
	93.0%	(/.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))))))
	53.1%	(/.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 #s(approx (/ (exp ( (neg cosTheta) cosTheta)) (* cosTheta c)) (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
	49.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 #s(approx (+ 1 (+ ( (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 c cosTheta)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) c)))
	90.3%	(exp.f32 (.f32 (log.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)))
✓	5.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (-.f32 (.f32 (neg.f32 cosTheta) (+.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32) (neg.f32 (.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (neg.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))))))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) cosTheta) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	97.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	96.9%	#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))
✓	93.8%	#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 1 702 to 1 382 computations (18.8% saved)

series41.0ms (1.2%)

Memory

-12.9MiB live, 85.7MiB allocated; 12ms collecting garbage

Counts

46 → 152

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

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

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta	@	0	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta) (* (/ 1 (sqrt (PI))) (PI)) (/ 1 (sqrt (PI))) (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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -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))) (/ (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)))) (/ (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (/ 1 (* (/ 1 (sqrt (PI))) (PI))))
7.0ms	cosTheta	@	-inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta) (* (/ 1 (sqrt (PI))) (PI)) (/ 1 (sqrt (PI))) (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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -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))) (/ (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)))) (/ (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (/ 1 (* (/ 1 (sqrt (PI))) (PI))))
5.0ms	cosTheta	@	inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta) (* (/ 1 (sqrt (PI))) (PI)) (/ 1 (sqrt (PI))) (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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -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))) (/ (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)))) (/ (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (/ 1 (* (/ 1 (sqrt (PI))) (PI))))
4.0ms	c	@	inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta) (* (/ 1 (sqrt (PI))) (PI)) (/ 1 (sqrt (PI))) (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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -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))) (/ (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)))) (/ (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (/ 1 (* (/ 1 (sqrt (PI))) (PI))))
3.0ms	c	@	-inf	((/ 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1))) 1 (+ (* (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (+ c 1)) (/ (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta)) (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (* (* (/ 1 (sqrt (PI))) (PI)) cosTheta) (* (/ 1 (sqrt (PI))) (PI)) (/ 1 (sqrt (PI))) (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)))) (/ (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 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 (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c)) (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/ (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) (+ (/ -1 (sqrt (PI))) c) (/ -1 (sqrt (PI))) -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))) (/ (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)))) (/ (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) cosTheta) (+ (* (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) cosTheta) (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) (/ 1 (* (/ 1 (sqrt (PI))) (PI))))

rewrite230.0ms (7%)

Memory

-0.6MiB live, 243.0MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	868	8911
0	931	7889
0	5320	7510

Stop Event

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

Counts

198 → 326

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

Outputs
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
(pow.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) 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 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta))) (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (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 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta))) (+.f32 c #s(literal 1 binary32))))
(/.f32 (+.f32 (pow.f32 (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (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 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta))) (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (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 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta))) (+.f32 c #s(literal 1 binary32))))))
(fma.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32)))
(+.f32 (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) 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)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.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 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
(.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)))
(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) cosTheta)
(/.f32 (neg.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))) (neg.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)))
(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.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 #s(literal -2 binary32) cosTheta) (.f32 #s(literal -2 binary32) cosTheta))) (-.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)))
(/.f32 (-.f32 (.f32 (-.f32 #s(literal 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 cosTheta cosTheta) (+.f32 cosTheta cosTheta))) (+.f32 #s(literal 1 binary32) (+.f32 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 (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 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 #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 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.f32 (PI.f32) cosTheta))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)
(.f32 cosTheta (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)))
(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32))
(*.f32 (PI.f32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 #s(literal 1 binary32) (PI.f32)) (sqrt.f32 (PI.f32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(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 (*.f32 c c) #s(literal 1 binary32)) (-.f32 c #s(literal 1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (*.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 (+.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 #s(literal -1 binary32) (neg.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal -1 binary32))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(/.f32 (neg.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (neg.f32 cosTheta))
(/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)
#s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 #s(literal -1 binary32) (neg.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal 1 binary32))))
(pow.f32 #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal 1 binary32))) #s(literal -1 binary32))
#s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+.f32 #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal 1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 #s(approx (+ ( (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))) (-.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))
(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 #s(approx (+ ( (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))) (.f32 #s(literal 1 binary32) #s(approx (+ ( (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))))))
(+.f32 #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
#s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta))
(/.f32 (neg.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (neg.f32 cosTheta))
(/.f32 (fma.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)
(+.f32 (/.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) cosTheta) (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta))
(+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) cosTheta) (/.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) cosTheta))
(/.f32 (-.f32 (.f32 (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta)) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) (-.f32 (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))
(/.f32 (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta))) (-.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (*.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta)))
(/.f32 (+.f32 (pow.f32 (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal 3 binary32))) (fma.f32 (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) (-.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))
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eval42.0ms (1.3%)

Memory: 0.6MiB live, 96.4MiB allocated; 12ms collecting garbage
Compiler: Compiled 8 151 to 2 114 computations (74.1% saved)

prune39.0ms (1.2%)

Memory

12.5MiB live, 105.1MiB allocated; 4ms collecting garbage

Pruning

30 alts after pruning (27 fresh and 3 done)

	Pruned	Kept	Total
New	330	12	342
Fresh	2	15	17
Picked	4	1	5
Done	2	2	4
Total	338	30	368

Accuracy

99.8%

Counts

368 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.1%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.5%	(/.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))))
	98.0%	(/.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))))
	98.4%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	98.2%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))
	93.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	93.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (* 1 (sqrt (- (- 1 cosTheta) cosTheta))) #s(literal 1 binary32)) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	97.3%	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 (fma.f32 (-.f32 (.f32 #s(literal -1/2 binary32) cosTheta) #s(literal 1 binary32)) cosTheta #s(literal 1 binary32)) cosTheta)) #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)))) (+.f32 c #s(literal 1 binary32))))
	97.5%	(/.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))))
	97.3%	(/.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 (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))))
	96.1%	(/.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 (+.f32 (neg.f32 cosTheta) #s(literal 1 binary32)) cosTheta)) (+.f32 c #s(literal 1 binary32))))
	92.9%	(/.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))))
	46.5%	(/.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) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta cosTheta)))))))
	97.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) #s(literal 1 binary32))))
	96.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(approx (+ (+ (neg (/ 1 (* (/ 1 (sqrt (PI))) (PI)))) c) 1) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta (/.f32 #s(literal 1 binary32) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (PI.f32)))) cosTheta)))
✓	93.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (+ (+ (neg (/ 1 (sqrt (PI)))) c) 1) cosTheta) (/ 1 (sqrt (PI)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))
	97.5%	(/.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 #s(approx (exp (* (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) cosTheta) c))))
	96.3%	(/.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))) #s(approx (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) c))))
	96.2%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (/.f32 (fma.f32 #s(approx (+ (/ -1 (sqrt (PI))) c) (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) cosTheta)))))
	97.4%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))))))))
	96.1%	(/.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) #s(approx (+ (* (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) c) #s(approx (/ (+ (* (+ (/ -1 (sqrt (PI))) c) cosTheta) (/ 1 (sqrt (PI)))) cosTheta) (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)) c))))))
	93.0%	(/.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))))))
	53.1%	(/.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 #s(approx (/ (exp ( (neg cosTheta) cosTheta)) (* cosTheta c)) (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta))) (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) c))) c)))
	49.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 #s(approx (+ 1 (+ ( (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (- (- 1 cosTheta) cosTheta) (PI)))) (/ 1 c))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 c cosTheta)) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) c)))
	90.3%	(exp.f32 (.f32 (log.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)))
✓	5.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (-.f32 (.f32 (neg.f32 cosTheta) (+.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (PI.f32) (neg.f32 (.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))) (neg.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)))))))))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) cosTheta) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	97.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -3/2 binary32)) (PI.f32) (neg.f32 (.f32 (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32))) (sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32))))))) (.f32 (+.f32 (+.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) c) #s(literal 1 binary32)) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	96.9%	#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))
✓	93.8%	#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 2 397 to 1 242 computations (48.2% saved)

regimes128.0ms (3.9%)

Memory

-34.9MiB live, 157.8MiB allocated; 8ms collecting garbage

Counts

59 → 1

Calls

Call 1

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

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

Calls

6 calls:

31.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
16.0ms	c
16.0ms	cosTheta
14.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
98.6%	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)))`
98.6%	1	`(+.f32 #s(literal 1 binary32) c)`
98.6%	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))))`
98.6%	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)))))`
98.6%	1	`cosTheta`
98.6%	1	`c`

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes62.0ms (1.9%)

Memory

26.5MiB live, 123.2MiB allocated; 8ms collecting garbage

Counts

37 → 1

Calls

Call 1

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

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)) #s(approx (exp ( (neg cosTheta) cosTheta)) (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32))) (+.f32 c #s(literal 1 binary32))))

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)) #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:

13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	c
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	(.f32 (.f32 (/.f32 #s(literal 1 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) c)

Results

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

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes34.0ms (1%)

Memory

-9.2MiB live, 81.6MiB allocated; 7ms collecting garbage

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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)))
6.0ms	cosTheta
5.0ms	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 #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
97.5%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.5%	1	`(+.f32 #s(literal 1 binary32) c)`
97.5%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.5%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.5%	1	`cosTheta`
97.5%	1	`c`

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes31.0ms (0.9%)

Memory

23.2MiB live, 68.4MiB allocated; 2ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

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:

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)))))
5.0ms	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	cosTheta

Results

Accuracy	Segments	Branch
97.3%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.3%	1	`(+.f32 #s(literal 1 binary32) c)`
97.3%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.3%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.3%	1	`cosTheta`
97.3%	1	`c`

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes44.0ms (1.3%)

Memory

4.7MiB live, 51.9MiB allocated; 24ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

#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))

Calls

6 calls:

20.0ms	cosTheta
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	c
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	(.f32 (.f32 (/.f32 #s(literal 1 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
96.9%	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)))`
96.9%	1	`(+.f32 #s(literal 1 binary32) c)`
96.9%	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))))`
96.9%	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)))))`
96.9%	1	`cosTheta`
96.9%	1	`c`

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes44.0ms (1.3%)

Memory

-7.0MiB live, 26.7MiB allocated; 19ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

6 calls:

30.0ms	(/.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	(+.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	c
3.0ms	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 60 to 58 computations (3.3% saved)

regimes15.0ms (0.5%)

Memory

24.6MiB live, 24.6MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	(/.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)))))
2.0ms	(.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)))
2.0ms	c
2.0ms	cosTheta

Results

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

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes22.0ms (0.7%)

Memory

-22.1MiB live, 23.3MiB allocated; 5ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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:

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))))
2.0ms	(/.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)))))
2.0ms	(.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)))
2.0ms	cosTheta
2.0ms	c

Results

Accuracy	Segments	Branch
93.8%	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)))))`
93.8%	1	`cosTheta`
93.8%	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)))`
93.8%	1	`(+.f32 #s(literal 1 binary32) c)`
93.8%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
93.8%	1	`c`

Compiler

Compiled 60 to 58 computations (3.3% saved)

regimes6.0ms (0.2%)

Memory

13.8MiB live, 13.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
5.1%	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)))))`
5.1%	1	`cosTheta`
5.1%	1	`c`
5.1%	1	`(+.f32 #s(literal 1 binary32) c)`
5.1%	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)))`
5.1%	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 60 to 58 computations (3.3% saved)

derivations218.0ms (6.6%)

Memory

10.0MiB live, 288.9MiB allocated; 55ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 196 to 90 computations (54.1% saved)

preprocess74.0ms (2.3%)

Memory: -22.0MiB live, 165.5MiB allocated; 41ms collecting garbage
Compiler: Compiled 217 to 108 computations (50.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze23.0ms (0.7%)

sample1.1s (33.7%)

preprocess51.0ms (1.6%)

series36.0ms (1.1%)

rewrite131.0ms (4%)

eval21.0ms (0.6%)

prune17.0ms (0.5%)

series48.0ms (1.5%)

rewrite337.0ms (10.3%)

eval104.0ms (3.2%)

prune39.0ms (1.2%)

series48.0ms (1.4%)

rewrite210.0ms (6.4%)

eval56.0ms (1.7%)

prune24.0ms (0.7%)

series41.0ms (1.2%)

rewrite230.0ms (7%)

eval42.0ms (1.3%)

prune39.0ms (1.2%)

regimes128.0ms (3.9%)

regimes62.0ms (1.9%)

regimes34.0ms (1%)

regimes31.0ms (0.9%)

regimes44.0ms (1.3%)

regimes44.0ms (1.3%)

regimes15.0ms (0.5%)

regimes22.0ms (0.7%)

regimes6.0ms (0.2%)

derivations218.0ms (6.6%)

preprocess74.0ms (2.3%)

end0.0ms (0%)

Profiling