Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

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

analyze25.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 41 to 29 computations (29.3% saved)

sample1.3s (6.1%)

Memory

29.2MiB live, 861.3MiB allocated; 141ms collecting garbage

Samples

931.0ms	8 256×	0	valid
9.0ms	64×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 746.0ms

ival-mult: 181.0ms (24.3% of total)

ival-div: 151.0ms (20.2% of total)

ival-sqrt: 109.0ms (14.6% of total)

ival-add: 82.0ms (11% of total)

ival-sub: 73.0ms (9.8% of total)

ival-exp: 63.0ms (8.4% of total)

ival-neg: 40.0ms (5.4% of total)

ival-pi: 32.0ms (4.3% of total)

exact: 8.0ms (1.1% of total)

adjust: 3.0ms (0.4% of total)

const: 2.0ms (0.3% of total)

ival-assert: 1.0ms (0.1% of total)

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

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

Bogosity

explain208.0ms (1%)

Memory

-23.2MiB live, 190.9MiB allocated; 30ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

64.0ms

512×

valid

Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions

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

ival-div: 10.0ms (22.7% of total)

ival-mult: 9.0ms (20.4% of total)

ival-sqrt: 6.0ms (13.6% of total)

ival-add: 5.0ms (11.3% of total)

ival-sub: 5.0ms (11.3% of total)

ival-exp: 4.0ms (9.1% of total)

ival-pi: 2.0ms (4.5% of total)

ival-neg: 2.0ms (4.5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess143.0ms (0.7%)

Memory

16.5MiB live, 154.8MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Compiler

Compiled 25 to 18 computations (28% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

97.8%

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

Compiler

Compiled 25 to 18 computations (28% saved)

series36.0ms (0.2%)

Memory

2.4MiB live, 47.4MiB allocated; 4ms collecting garbage

Counts

18 → 111

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	cosTheta	@	inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
10.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
3.0ms	cosTheta	@	0	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
3.0ms	c	@	0	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))
1.0ms	c	@	inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (/ 1 (sqrt (PI))) (sqrt (PI)) (PI) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (- (- 1 cosTheta) cosTheta) (- 1 cosTheta) cosTheta (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta))

rewrite140.0ms (0.7%)

Memory

13.7MiB live, 154.8MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

129 → 177

Calls

Call 1

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

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

eval20.0ms (0.1%)

Memory: -23.2MiB live, 23.4MiB allocated; 2ms collecting garbage
Compiler: Compiled 8 637 to 1 127 computations (87% saved)

prune132.0ms (0.6%)

Memory

-17.4MiB live, 77.4MiB allocated; 2ms collecting garbage

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	182	7	189

Accuracy

99.4%

Counts

189 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.9%	(/.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 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))) (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))))) (-.f32 (+.f32 c #s(literal 1 binary32)) (.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))))))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	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)))))
▶	53.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (+.f32 (fma.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 cosTheta c)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
▶	54.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (neg.f32 (.f32 (-.f32 (neg.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) c)) #s(literal 1 binary32)) c))))
▶	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
▶	96.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))

Compiler

Compiled 671 to 370 computations (44.9% saved)

series159.0ms (0.7%)

Memory

11.8MiB live, 106.3MiB allocated; 8ms collecting garbage

Counts

53 → 442

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
47.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) 3 (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) 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 (* (- (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) 1) c)) (* (- (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) 1) c) (- (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) 1) (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) 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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c) (/ 1 c))
35.0ms	cosTheta	@	inf	((/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) c (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta) (sqrt (+ (* -2 cosTheta) 1)) (+ (* -2 cosTheta) 1) -2 cosTheta (sqrt (PI)) (PI) (exp (* (neg cosTheta) cosTheta)) (* (neg cosTheta) cosTheta) (neg cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI)) (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (+ (* (/ 1 (sqrt (PI))) -1) c) (/ 1 (sqrt (PI))) -1 (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (+ (* -2 cosTheta) 1) (PI)) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta) 3 (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) 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 (* (- (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) 1) c)) (* (- (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) 1) c) (- (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) 1) (neg (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) c)) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) 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)))) (* (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) c) (+ (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) 1) (+ (* (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (* cosTheta c) (/ 1 c))
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rewrite288.0ms (1.4%)

Memory

20.8MiB live, 208.7MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2300	50955
0	2399	48614
0	8436	47666

Stop Event

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

Counts

495 → 546

Calls

Call 1

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

eval123.0ms (0.6%)

Memory: -16.2MiB live, 124.2MiB allocated; 16ms collecting garbage
Compiler: Compiled 95 854 to 5 058 computations (94.7% saved)

prune2.4s (11.2%)

Memory

5.8MiB live, 1 829.8MiB allocated; 102ms collecting garbage

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	899	11	910
Fresh	1	0	1
Picked	3	2	5
Done	0	1	1
Total	903	14	917

Accuracy

99.9%

Counts

917 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 (cosh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))))
✓	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)))))
	53.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (+.f32 (fma.f32 #s(approx (/ (exp ( (neg cosTheta) cosTheta)) (* cosTheta c)) (/.f32 (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal -1/6 binary32) (/.f32 (.f32 cosTheta cosTheta) c) (*.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) c)))) (/.f32 #s(literal 1 binary32) c)) (/.f32 #s(literal 1 binary32) c)) cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) #s(literal 1 binary32)) c)))
	53.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (.f32 (+.f32 #s(approx (+ ( (/ (exp (* (neg cosTheta) cosTheta)) (* cosTheta c)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 c)) (/.f32 (fma.f32 cosTheta (fma.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (fma.f32 cosTheta (fma.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (fma.f32 #s(literal -1/2 binary32) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (.f32 cosTheta (fma.f32 #s(literal -1/2 binary32) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))) (/.f32 #s(literal 1 binary32) c))) (*.f32 (/.f32 #s(literal 1 binary32) c) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) cosTheta)) #s(literal 1 binary32)) c)))
✓	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
▶	97.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
✓	96.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	95.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))) cosTheta))
▶	95.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) c) (.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32))))))) cosTheta))
	95.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 #s(literal -1 binary32) (.f32 c (fma.f32 #s(literal -1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))))) c) (*.f32 cosTheta (PI.f32)))))) cosTheta))
▶	57.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32)))))))) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))))))
	56.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32))))))))
▶	54.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) (fma.f32 #s(literal -1 binary32) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) (*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))))

Compiler

Compiled 2 262 to 1 093 computations (51.7% saved)

series303.0ms (1.4%)

Memory

18.7MiB live, 204.0MiB allocated; 14ms collecting garbage

Counts

82 → 544

Calls

Call 1

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

Outputs
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (+ (cosh (* (neg cosTheta) cosTheta)) (sinh (* (neg cosTheta) cosTheta)))))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (+ (cosh (* (neg cosTheta) cosTheta)) (sinh (* (neg cosTheta) cosTheta)))))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (+ (cosh (* (neg cosTheta) cosTheta)) (sinh (* (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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Calls

6 calls:

Time	Variable		Point	Expression
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rewrite403.0ms (1.9%)

Memory

17.3MiB live, 302.5MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3323	89617
0	3471	84756
0	11112	83161

Stop Event

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

Counts

626 → 715

Calls

Call 1

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

eval184.0ms (0.9%)

Memory: 0.0MiB live, 181.4MiB allocated; 26ms collecting garbage
Compiler: Compiled 194 847 to 7 397 computations (96.2% saved)

prune3.6s (16.9%)

Memory

-31.2MiB live, 2 900.6MiB allocated; 82ms collecting garbage

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	1 105	5	1 110
Fresh	4	2	6
Picked	1	4	5
Done	0	3	3
Total	1 110	14	1 124

Accuracy

99.9%

Counts

1 124 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 (cosh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))))
✓	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)))))
	54.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (+ (cosh (* (neg cosTheta) cosTheta)) (sinh (* (neg cosTheta) cosTheta))))) (.f32 #s(literal -1 binary32) (.f32 c (-.f32 (.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (+.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) (exp.f32 (neg.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))) (.f32 #s(literal 1/2 binary32) (-.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) (exp.f32 (neg.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))))) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) c)) #s(literal 1 binary32))))))
✓	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
▶	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
✓	97.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
✓	96.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	95.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))) cosTheta))
✓	95.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) c) (.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32))))))) cosTheta))
▶	45.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) #s(approx (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))) c) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta)) (sqrt.f32 (PI.f32))))))))) cosTheta))
✓	57.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32)))))))) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))))))
▶	54.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) #s(approx (/ 1 ( c (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))) (.f32 (/.f32 cosTheta c) (sqrt.f32 (PI.f32))))) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))))))
▶	56.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32))))))))
▶	54.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))))) cosTheta)))))

Compiler

Compiled 2 115 to 1 029 computations (51.3% saved)

series279.0ms (1.3%)

Memory

34.1MiB live, 219.8MiB allocated; 13ms collecting garbage

Counts

99 → 634

Calls

Call 1

Inputs
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
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c
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(fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) #s(approx (/ 1 ( c (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))) (.f32 (/.f32 cosTheta c) (sqrt.f32 (PI.f32))))) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32)))
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(-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) #s(approx (/ 1 ( c (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))) (*.f32 (/.f32 cosTheta c) (sqrt.f32 (PI.f32)))))
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(/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) cosTheta)
(pow.f32 (exp.f32 #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
#s(approx (/ 1 (* c (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))) (*.f32 (/.f32 cosTheta c) (sqrt.f32 (PI.f32))))
(*.f32 (/.f32 cosTheta c) (sqrt.f32 (PI.f32)))
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(pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) #s(approx (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))) c) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta)) (sqrt.f32 (PI.f32))))))))) cosTheta))
(.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) #s(approx (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))) c) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta)) (sqrt.f32 (PI.f32))))))))) cosTheta)
#s(approx (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) #s(approx (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))) c) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta)) (sqrt.f32 (PI.f32)))))))))
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(fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) #s(approx (+ ( -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))) c) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta)) (sqrt.f32 (PI.f32)))))))
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(*.f32 c 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 (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) #s(hole binary32 (* cosTheta (sqrt (PI)))))
#s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* c (PI))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))))
#s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* -1 (* c (PI))) (* cosTheta (- (* c (+ (* 2 (* (sqrt (pow (PI) 3)) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* c (sqrt (pow (PI) 3))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))))
#s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) #s(hole binary32 (* cosTheta (+ (sqrt (PI)) (* cosTheta (- (+ (* -1 (* c (PI))) (* cosTheta (- (+ (* c (+ (* 2 (* (sqrt (pow (PI) 3)) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* c (sqrt (pow (PI) 3))))) (* cosTheta (- (* c (- (+ (* -4 (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (pow (PI) 2) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))) (* c (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ 1 (PI)))))))) (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))))
#s(approx (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) #s(hole binary32 (* -1 (* (pow cosTheta 2) (PI)))))
#s(approx (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) #s(hole binary32 (* (pow cosTheta 2) (- (* cosTheta (+ (* 2 (* (sqrt (pow (PI) 3)) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (* c (sqrt (pow (PI) 3))))) (PI)))))
#s(approx (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) #s(hole binary32 (* (pow cosTheta 2) (- (* cosTheta (+ (* 2 (* (sqrt (pow (PI) 3)) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (+ (* c (sqrt (pow (PI) 3))) (* cosTheta (- (+ (* -4 (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (pow (PI) 2) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2)))) (* c (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ 1 (PI))))))))))) (PI)))))
#s(approx (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) #s(hole binary32 (* (pow cosTheta 2) (- (* cosTheta (+ (* 2 (* (sqrt (pow (PI) 3)) (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (+ (* c (sqrt (pow (PI) 3))) (* cosTheta (- (+ (* -4 (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (+ (* cosTheta (- (+ (* -2 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -4 (* (pow (PI) 2) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (pow (PI) 2) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))))) (+ (* -2 (* (sqrt (pow (PI) 5)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) (* (pow (PI) 2) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))) (* 2 (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) (+ (* -1 (* (* c (pow (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ 1 (PI)))) 2)) (sqrt (pow (PI) 9)))) (* c (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* -1/2 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (* (sqrt (/ 1 (PI))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (sqrt (/ 1 (PI))) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))))))))) (* (pow (PI) 2) (+ (* 2 (* (sqrt (/ 1 (PI))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))))) (* c (* (pow (PI) 3) (+ (* -1 (sqrt (/ 1 (pow (PI) 3)))) (+ (* 2 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) (PI))) (/ 1 (PI))))))))))) (PI)))))
#s(approx (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) #s(hole binary32 (* (* c (pow cosTheta 3)) (sqrt (pow (PI) 3)))))
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Calls

6 calls:

Time	Variable		Point	Expression
48.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 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cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (pow (exp -1) (* cosTheta cosTheta)) (/ 1 (* c (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))) (* (/ cosTheta c) (sqrt (PI))) (/ cosTheta c) (pow (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) -3) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (* c (+ (* -1 (* cosTheta (PI))) (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))))) (+ (* -1 (* cosTheta (PI))) (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI))))) (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (* cosTheta (+ (* -1 (/ (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI)))))) c)) (* (/ 1 (* c cosTheta)) (sqrt (PI))))) (+ (* -1 (/ (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI)))))) c)) (* (/ 1 (* c cosTheta)) (sqrt (PI)))) (/ (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI)))))) c) (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI)))))) (+ 1 (* -1 (/ 1 (sqrt (PI))))) (* (/ 1 (* c cosTheta)) (sqrt (PI))) (/ 1 (* c cosTheta)) (* c cosTheta))

rewrite508.0ms (2.4%)

Memory

-5.9MiB live, 506.9MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3602	123172
0	3767	117226
0	12541	115037

Stop Event

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

Counts

733 → 834

Calls

Call 1

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

eval221.0ms (1%)

Memory: 30.6MiB live, 263.3MiB allocated; 25ms collecting garbage
Compiler: Compiled 273 058 to 8 961 computations (96.7% saved)

prune10.4s (48.8%)

Memory

6.7MiB live, 12 828.6MiB allocated; 172ms collecting garbage

Pruning

14 alts after pruning (2 fresh and 12 done)

	Pruned	Kept	Total
New	1 304	0	1 304
Fresh	0	2	2
Picked	0	5	5
Done	0	7	7
Total	1 304	14	1 318

Accuracy

99.9%

Counts

1 318 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 (cosh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))))
✓	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)))))
	54.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (* 1 (/ (sqrt (+ (* -2 cosTheta) 1)) cosTheta)) (sqrt (PI))) (+ (cosh (* (neg cosTheta) cosTheta)) (sinh (* (neg cosTheta) cosTheta))))) (.f32 #s(literal -1 binary32) (.f32 c (-.f32 (.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (+.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) (exp.f32 (neg.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))) (.f32 #s(literal 1/2 binary32) (-.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) (exp.f32 (neg.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))))) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) c)) #s(literal 1 binary32))))))
✓	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
✓	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
✓	97.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
✓	96.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	95.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))) cosTheta))
✓	95.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) c) (.f32 (/.f32 #s(literal 1 binary32) c) (sqrt.f32 (PI.f32))))))) cosTheta))
✓	45.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 c (fma.f32 #s(literal -1 binary32) (.f32 cosTheta (PI.f32)) #s(approx (+ (* -1 (/ (* cosTheta (* (PI) (+ 1 (* -1 (/ 1 (sqrt (PI))))))) c)) (* (/ 1 c) (sqrt (PI)))) (.f32 cosTheta (fma.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))) c) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 c cosTheta)) (sqrt.f32 (PI.f32))))))))) cosTheta))
✓	57.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) (/.f32 #s(literal 1 binary32) (.f32 c (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32)))))))) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))))))
✓	54.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -2 binary32)) #s(approx (/ 1 ( c (+ 1 (* (/ (pow (exp -1) (* cosTheta cosTheta)) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))) (.f32 (/.f32 cosTheta c) (sqrt.f32 (PI.f32))))) c) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))))))
✓	56.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) cosTheta) cosTheta) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (*.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32))))))))
✓	54.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))))) cosTheta)))))

Compiler

Compiled 3 348 to 977 computations (70.8% saved)

regimes38.0ms (0.2%)

Memory

-16.5MiB live, 30.7MiB allocated; 1ms collecting garbage

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

7.0ms	cosTheta
6.0ms	c
6.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
6.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
6.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes35.0ms (0.2%)

Memory

-18.7MiB live, 28.7MiB allocated; 1ms collecting garbage

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes33.0ms (0.2%)

Memory

27.9MiB live, 27.9MiB allocated; 0ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

5.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
5.0ms	(/.f32 #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 (/.f32 #s(literal 1 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
97.8%	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)))`
97.8%	1	`(+.f32 #s(literal 1 binary32) c)`
97.8%	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))))`
97.8%	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)))))`
97.8%	1	`cosTheta`
97.8%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes23.0ms (0.1%)

Memory

-25.1MiB live, 22.5MiB allocated; 1ms collecting garbage

Counts

12 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

4.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
4.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms	cosTheta
4.0ms	c

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 (+.f32 #s(literal 1 binary32) 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	`c`
97.5%	1	`(+.f32 #s(literal 1 binary32) c)`
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`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes21.0ms (0.1%)

Memory

21.1MiB live, 21.1MiB allocated; 0ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes19.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
95.8%	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)))`
95.8%	1	`(+.f32 #s(literal 1 binary32) c)`
95.8%	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))))`
95.8%	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)))))`
95.8%	1	`cosTheta`
95.8%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes15.0ms (0.1%)

Memory

-33.4MiB live, 16.0MiB allocated; 1ms collecting garbage

Counts

6 → 3

Calls

Call 1

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

Outputs

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

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

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

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 (.f32 (/.f32 #s(literal 1 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	cosTheta
2.0ms	c

Results

Accuracy	Segments	Branch
73.5%	2	`(/.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)))))`
73.5%	2	`cosTheta`
77.2%	3	`c`
73.5%	2	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
57.3%	1	`(+.f32 #s(literal 1 binary32) c)`
73.5%	2	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes8.0ms (0%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.1b remaining (-0.5%)

Threshold costs -0.1b (-0.5%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs

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

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	cosTheta
1.0ms	c

Results

Accuracy	Segments	Branch
54.9%	1	`(+.f32 #s(literal 1 binary32) c)`
54.9%	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)))`
54.9%	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))))`
54.9%	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)))))`
54.9%	1	`cosTheta`
54.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

bsearch1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
0.0ms	1.2918625208753571e-23	2.1508470547871105e-22
0.0ms	-7.040067348521154e-23	-2.5032279394879707e-23

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify49.0ms (0.2%)

Memory

-19.6MiB live, 27.2MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	718
1	271	685
2	699	675
3	2860	671

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 (cosh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 #s(literal -1 binary32) (.f32 c (fma.f32 #s(literal -1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))))) c) (*.f32 cosTheta (PI.f32)))))) cosTheta))
(if (<=.f32 c #s(literal -15845633/316912650057057350374175801344 binary32)) #s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32)))))))) (if (<=.f32 c #s(literal 6338253/316912650057057350374175801344 binary32)) #s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))))) cosTheta))))) #s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32))))))))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))))) cosTheta)))))

Outputs
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 (cosh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 (cosh.f32 (.f32 cosTheta cosTheta)) (sinh.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (/ (+ (* -2 cosTheta) 1) (PI)) (.f32 cosTheta (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta (PI.f32))) (.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))))))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (fma.f32 (-.f32 (/.f32 c (pow.f32 (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) (.f32 (/.f32 #s(literal 1 binary32) cosTheta) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))) #s(literal -2 binary32))) c (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (neg.f32 cosTheta) (.f32 (+.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) #s(literal -1 binary32) c) #s(literal 1 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 #s(literal -1 binary32) (.f32 c (fma.f32 #s(literal -1 binary32) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))))) c) (*.f32 cosTheta (PI.f32)))))) cosTheta))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 #s(approx (+ ( (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) (.f32 (neg.f32 c) (fma.f32 #s(literal -1 binary32) (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))))) c) (.f32 cosTheta (PI.f32))))) cosTheta))
(if (<=.f32 c #s(literal -15845633/316912650057057350374175801344 binary32)) #s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32)))))))) (if (<=.f32 c #s(literal 6338253/316912650057057350374175801344 binary32)) #s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))))) cosTheta))))) #s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (+ (* (- (/ c (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) 3)) (pow (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1) -2)) c) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (exp (* (neg cosTheta) cosTheta)) cosTheta)) 1))) (.f32 (.f32 c c) (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 c c) (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))))) (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal -3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 c (pow.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (pow.f32 (exp.f32 #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) cosTheta) (sqrt.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) cosTheta)) (PI.f32))))) #s(literal 2 binary32))))))))))
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#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (+.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (+.f32 c (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))))) cosTheta)))))
#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (* (+ (* (neg cosTheta) (* (+ (+ (* (/ 1 (sqrt (PI))) -1) c) 1) (PI))) (sqrt (PI))) cosTheta) (.f32 (.f32 cosTheta cosTheta) #s(approx (+ (* -1 (* (PI) (+ 1 (+ c (* -1 (/ 1 (sqrt (PI)))))))) (* (/ 1 cosTheta) (sqrt (PI)))) (/.f32 (-.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (-.f32 c (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))))))) cosTheta)))))

derivations154.0ms (0.7%)

Memory

0.7MiB live, 43.9MiB allocated; 5ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 717 to 160 computations (77.7% saved)

preprocess49.0ms (0.2%)

Memory: -0.4MiB live, 46.2MiB allocated; 4ms collecting garbage
Compiler: Compiled 1 484 to 356 computations (76% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze25.0ms (0.1%)

sample1.3s (6.1%)

explain208.0ms (1%)

preprocess143.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

series36.0ms (0.2%)

rewrite140.0ms (0.7%)

eval20.0ms (0.1%)

prune132.0ms (0.6%)

series159.0ms (0.7%)

rewrite288.0ms (1.4%)

eval123.0ms (0.6%)

prune2.4s (11.2%)

series303.0ms (1.4%)

rewrite403.0ms (1.9%)

eval184.0ms (0.9%)

prune3.6s (16.9%)

series279.0ms (1.3%)

rewrite508.0ms (2.4%)

eval221.0ms (1%)

prune10.4s (48.8%)

regimes38.0ms (0.2%)

regimes35.0ms (0.2%)

regimes33.0ms (0.2%)

regimes23.0ms (0.1%)

regimes21.0ms (0.1%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes8.0ms (0%)

bsearch1.0ms (0%)

simplify49.0ms (0.2%)

derivations154.0ms (0.7%)

preprocess49.0ms (0.2%)

end0.0ms (0%)

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