Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

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

analyze30.0ms (0.3%)

Memory

14.1MiB live, 58.3MiB allocated; 9ms 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)

sample2.3s (24.6%)

Memory

105.2MiB live, 3 568.8MiB allocated; 680ms collecting garbage

Samples

1.7s	8 256×	0	valid
8.0ms	54×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-div: 204.0ms (15.8% of total)

ival-mult: 191.0ms (14.8% of total)

ival-<: 180.0ms (13.9% of total)

ival-sqrt: 147.0ms (11.4% of total)

const: 145.0ms (11.2% of total)

ival-add: 123.0ms (9.5% of total)

ival-sub: 90.0ms (7% of total)

ival-exp: 76.0ms (5.9% of total)

ival-pi: 50.0ms (3.9% of total)

ival-neg: 37.0ms (2.9% of total)

ival-and: 25.0ms (1.9% of total)

exact: 16.0ms (1.2% of total)

ival-assert: 4.0ms (0.3% of total)

adjust: 3.0ms (0.2% of total)

Bogosity

explain245.0ms (2.7%)

Memory

11.3MiB live, 484.4MiB allocated; 100ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

93.0ms

512×

valid

Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-neg: 13.0ms (23.1% of total)

ival-mult: 11.0ms (19.5% of total)

ival-div: 9.0ms (16% of total)

ival-sqrt: 6.0ms (10.7% of total)

ival-add: 5.0ms (8.9% of total)

ival-sub: 5.0ms (8.9% of total)

ival-exp: 4.0ms (7.1% of total)

ival-pi: 2.0ms (3.6% 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)

preprocess164.0ms (1.8%)

Memory

-8.9MiB live, 276.4MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	133
1	138	119
2	473	112
3	2127	110
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)

prune1.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.7%	(/.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

▶

97.7%

(/.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)

simplify150.0ms (1.6%)

Memory

4.8MiB live, 200.3MiB allocated; 68ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	126
0	33	126
1	60	118
2	173	115
3	742	115
4	3742	115
0	8784	108

Stop Event

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

localize47.0ms (0.5%)

Memory

1.2MiB live, 92.4MiB allocated; 8ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.09603500976844201	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.29296875	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.6051750488422102	(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))
accuracy	1.0	(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))

Samples

35.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-div: 7.0ms (29.5% of total)

ival-mult: 4.0ms (16.8% of total)

ival-add: 3.0ms (12.6% of total)

ival-sqrt: 3.0ms (12.6% of total)

ival-exp: 2.0ms (8.4% of total)

ival-sub: 2.0ms (8.4% of total)

ival-pi: 1.0ms (4.2% of total)

ival-neg: 1.0ms (4.2% 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)

series27.0ms (0.3%)

Memory

-16.4MiB live, 40.4MiB allocated; 11ms collecting garbage

Counts

5 → 50

Calls

Call 1

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

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 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 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -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))))))
(- (+ (* -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)))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	cosTheta	@	-inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
6.0ms	cosTheta	@	inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
2.0ms	cosTheta	@	0	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
1.0ms	c	@	0	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))
1.0ms	c	@	inf	((* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (sqrt (PI))))

simplify182.0ms (2%)

Memory

33.7MiB live, 307.3MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	378	2856
1	1220	2772
2	5849	2705
0	8690	2591

Stop Event

1×	iter limit
1×	node limit

Counts

50 → 50

Calls

Call 1

Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (pow (sqrt 2) 3)))))))
(* -1 (* cosTheta (- 2 (/ 1 cosTheta))))
(/ 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 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
(- (+ (* -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))))))
(- (+ (* -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)))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))

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

rewrite103.0ms (1.1%)

Memory

-16.1MiB live, 130.8MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	66
0	33	66
1	133	59
0	1016	58

Stop Event

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

Counts

5 → 69

Calls

Call 1

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

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

eval17.0ms (0.2%)

Memory: 25.2MiB live, 69.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 5 885 to 830 computations (85.9% saved)

prune13.0ms (0.1%)

Memory

3.8MiB live, 48.5MiB allocated; 4ms collecting garbage

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	15	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	15	120

Accuracy

99.6%

Counts

120 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 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 #s(approx (- (- 1 cosTheta) cosTheta) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 2 binary32)) cosTheta))) cosTheta)) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	90.8%	(/.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 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (fma.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
▶	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	98.0%	(*.f32 (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
	55.6%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))))))
	90.5%	(exp.f32 (*.f32 (log1p.f32 (fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) c)) #s(literal -1 binary32)))
▶	97.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
▶	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	96.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32))))) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta))
	94.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
	91.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))

Compiler

Compiled 1 122 to 724 computations (35.5% saved)

simplify257.0ms (2.8%)

Memory

-51.2MiB live, 340.5MiB allocated; 41ms collecting garbage

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	585
0	100	586
1	167	557
2	381	546
3	1173	542
4	5318	542
0	8231	542

Stop Event

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

Calls

Call 1

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

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

localize165.0ms (1.8%)

Memory

24.9MiB live, 217.6MiB allocated; 18ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.10176630544920161	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
accuracy	0.296875	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)))
accuracy	0.5504875488422101	(fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))
accuracy	0.80078125	(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
accuracy	0.0625	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)
accuracy	0.09603500976844201	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.29296875	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.3984375	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	0.55078125	(/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.6179276367581885	(.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta))
accuracy	0.7226707303502655	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	0.0	(/.f32 #s(literal 1 binary32) c)
accuracy	30.43004309935548	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy	0.09603500976844201	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.29296875	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.328125	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3984375	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Samples

108.0ms

256×

valid

Compiler

Compiled 507 to 50 computations (90.1% saved)

Precisions

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

ival-pow: 27.0ms (30.6% of total)

ival-div: 19.0ms (21.5% of total)

ival-mult: 18.0ms (20.4% of total)

ival-add: 8.0ms (9.1% of total)

ival-sqrt: 6.0ms (6.8% of total)

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

ival-sub: 3.0ms (3.4% of total)

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

ival-neg: 1.0ms (1.1% 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)

series68.0ms (0.7%)

Memory

-20.1MiB live, 72.1MiB allocated; 22ms collecting garbage

Counts

24 → 120

Calls

Call 1

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

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 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))))))
(+ 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)))))))
(+ 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))))))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))))
(/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* (sqrt (/ 1 cosTheta)) (sqrt -2))
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(/ 1 c)
(+ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (/ 1 c)))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	cosTheta	@	inf	((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
9.0ms	cosTheta	@	-inf	((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
5.0ms	cosTheta	@	0	((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
2.0ms	c	@	0	((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))
1.0ms	c	@	-inf	((* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (- (- 1 cosTheta) cosTheta) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta))

simplify320.0ms (3.5%)

Memory

-1.2MiB live, 303.1MiB allocated; 112ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	652	6136
1	2221	5922
0	8591	5687

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 119

Calls

Call 1

Inputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
1
(+ 1 (* -2 cosTheta))
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(* -2 cosTheta)
(* cosTheta (- (/ 1 cosTheta) 2))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))) (* (sqrt -2) (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))))) (+ (* 1/16 (* (sqrt (/ (pow cosTheta 5) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 5) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/16 (/ (* (pow cosTheta 2) (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 4) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (+ (* -1/4 (/ (pow (exp (* -1 (pow cosTheta 2))) 2) (* (pow cosTheta 3) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ 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))))))
(+ 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)))))))
(+ 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))))))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))))))
(/ 1 (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))
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(/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
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(* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))
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(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/ 1 c)
(+ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (/ 1 c)))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))

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

rewrite248.0ms (2.7%)

Memory

-24.8MiB live, 222.3MiB allocated; 55ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	60	447
0	100	447
1	364	379
2	2737	379
0	8191	379

Stop Event

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

Counts

24 → 718

Calls

Call 1

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

Outputs
(.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (/.f32 cosTheta #s(literal -2 binary32)))) (pow.f32 (exp.f32 cosTheta) (/.f32 cosTheta #s(literal -2 binary32))))
(.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))
(.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(.f32 (pow.f32 (exp.f32 cosTheta) (/.f32 cosTheta #s(literal -2 binary32))) (.f32 (pow.f32 (exp.f32 cosTheta) (/.f32 cosTheta #s(literal -2 binary32))) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)))
(.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1 binary32)))
(*.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))
(.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)))
(*.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))
(.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))))
(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
(*.f32 (/.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)) #s(literal 1 binary32))
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(*.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))
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(*.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32)))))
(*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(*.f32 (pow.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 1/2 binary32)) (pow.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32)) #s(literal 1/2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal -1/2 binary32)) (pow.f32 (neg.f32 (sqrt.f32 (PI.f32))) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal -1/2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -1/2 binary32)) (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) (pow.f32 (PI.f32) #s(literal -1/4 binary32)))
(*.f32 (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal -1 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 (neg.f32 (sqrt.f32 #s(literal -1 binary32))) (neg.f32 (sqrt.f32 (neg.f32 (PI.f32)))))
(/.f32 (fabs.f32 (sqrt.f32 #s(literal -1 binary32))) (fabs.f32 (sqrt.f32 (neg.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (*.f32 #s(literal -1 binary32) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (sqrt.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal -1 binary32))) (sqrt.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -2 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(/.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(/.f32 (sqrt.f32 #s(literal -1 binary32)) (sqrt.f32 (neg.f32 (PI.f32))))
(/.f32 #s(literal -1 binary32) (neg.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 #s(literal 1 binary32) (fabs.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (neg.f32 (neg.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))) #s(literal -1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal -2 binary32)) #s(literal 1/4 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) #s(literal -1/6 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/4 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal -1 binary32))
(pow.f32 (PI.f32) #s(literal -1/2 binary32))
(fabs.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
(fabs.f32 (neg.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(fabs.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(+.f32 (cosh.f32 (.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32)))) (sinh.f32 (.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32)))))
(exp.f32 (fma.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32)) #s(literal 0 binary32)))
(exp.f32 (/.f32 (neg.f32 (log.f32 (PI.f32))) #s(literal 2 binary32)))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal -1/2 binary32)))
(exp.f32 (*.f32 #s(literal -1/2 binary32) (log.f32 (PI.f32))))
(neg.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))
(log.f32 (pow.f32 (exp.f32 cosTheta) (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32)))))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) #s(literal -3/2 binary32))
(*.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) cosTheta)
(.f32 (.f32 #s(literal -3/2 binary32) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(.f32 #s(literal -3/2 binary32) (.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))))
(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (.f32 #s(literal -3/2 binary32) cosTheta))
(*.f32 cosTheta (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (.f32 #s(literal -1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta))) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal -1 binary32))) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal -1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal -1 binary32)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))
(*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta))
(/.f32 (neg.f32 (*.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (neg.f32 (neg.f32 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 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) #s(literal -1 binary32))) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (neg.f32 (.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) #s(literal -1 binary32))) (neg.f32 (.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 (neg.f32 (.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) #s(literal -1 binary32))) (neg.f32 (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (.f32 (neg.f32 (sqrt.f32 (PI.f32))) (neg.f32 cosTheta))))
(/.f32 (neg.f32 (.f32 #s(literal -1 binary32) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (neg.f32 (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (neg.f32 (.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) #s(literal 1 binary32))) (neg.f32 (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (neg.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))))
(/.f32 (neg.f32 (.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (*.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (neg.f32 cosTheta))
(/.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))))
(/.f32 (*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) #s(literal -1 binary32)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (neg.f32 cosTheta))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (neg.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))) (neg.f32 cosTheta))
(/.f32 (.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) #s(literal -1 binary32)) (.f32 (neg.f32 cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) #s(literal 1 binary32)) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) #s(literal -1 binary32)) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal -1 binary32) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (.f32 (neg.f32 (sqrt.f32 (PI.f32))) (neg.f32 cosTheta)))
(/.f32 (.f32 #s(literal -1 binary32) (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)) (neg.f32 (neg.f32 (neg.f32 (sqrt.f32 (PI.f32))))))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (neg.f32 (neg.f32 (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (neg.f32 cosTheta)))
(*.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta))
(/.f32 (neg.f32 (neg.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (neg.f32 (neg.f32 cosTheta))))
(/.f32 (neg.f32 (*.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (*.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (neg.f32 cosTheta))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (neg.f32 cosTheta))
(/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) cosTheta)
(neg.f32 (/.f32 (sqrt.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))) (neg.f32 cosTheta)))

eval166.0ms (1.8%)

Memory: 29.6MiB live, 162.5MiB allocated; 32ms collecting garbage
Compiler: Compiled 38 280 to 4 048 computations (89.4% saved)

prune68.0ms (0.7%)

Memory

-15.9MiB live, 84.4MiB allocated; 17ms collecting garbage

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	767	29	796
Fresh	10	0	10
Picked	3	2	5
Done	0	0	0
Total	780	31	811

Accuracy

99.9%

Counts

811 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.8%	(pow.f32 (pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	53.5%	(pow.f32 (.f32 (+.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32))) (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal -1/2 binary32))
▶	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	95.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	91.4%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))))) cosTheta))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))) cosTheta))))
	56.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta) cosTheta (.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (*.f32 cosTheta cosTheta)))))
	96.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (-.f32 (pow.f32 (.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (-.f32 (.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (*.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)))))
	52.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -1 binary32) cosTheta) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta))) cosTheta)))))
	52.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta))) (neg.f32 cosTheta))))))))
	54.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) c #s(literal 1 binary32))))
	97.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (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) (+.f32 #s(literal 1 binary32) c))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)) cosTheta) #s(literal 1 binary32))))
	95.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) c)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	94.2%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (-.f32 (+.f32 #s(literal 1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	55.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (.f32 (neg.f32 c) (-.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)) (neg.f32 c)) #s(literal 1 binary32)))))
	53.4%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
	94.8%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
▶	91.9%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
▶	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
	96.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
▶	95.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	94.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (+.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))))
✓	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	95.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (.f32 (fma.f32 (-.f32 (.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (.f32 (PI.f32) #s(literal -3/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) (*.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)))
	94.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (.f32 (fma.f32 (neg.f32 (.f32 (PI.f32) cosTheta)) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))) cosTheta)))

Compiler

Compiled 3 004 to 1 902 computations (36.7% saved)

simplify229.0ms (2.5%)

Memory

27.4MiB live, 218.6MiB allocated; 49ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	586
0	118	586
1	211	574
2	573	571
3	2006	557
0	8650	547

Stop Event

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

Calls

Call 1

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

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

localize341.0ms (3.7%)

Memory

-0.6MiB live, 380.9MiB allocated; 32ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0625	(/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32))
accuracy	0.10176630544920161	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
accuracy	0.296875	(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)))
accuracy	0.5504875488422101	(fma.f32 (/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))
accuracy	0.046875	(.f32 (/.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))
accuracy	0.29296875	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.3984375	(/.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32)))
accuracy	2.3606417887509235	#s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta))
accuracy	0.546875	(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.6996897029924596	#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy	0.9997126586104002	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	0.0	(sqrt.f32 (PI.f32))
accuracy	0.0	(PI.f32)
accuracy	0.3984375	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	2.244257367268601	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.08203125	(/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))
accuracy	0.29296875	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.5390625	(/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta)
accuracy	0.80078125	(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))

Samples

272.0ms

256×

valid

Compiler

Compiled 490 to 64 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 252.0ms

ival-mult: 125.0ms (49.7% of total)

ival-div: 90.0ms (35.8% of total)

ival-add: 13.0ms (5.2% of total)

ival-sqrt: 8.0ms (3.2% of total)

ival-pow: 6.0ms (2.4% of total)

ival-exp: 4.0ms (1.6% of total)

ival-sub: 2.0ms (0.8% of total)

ival-pi: 1.0ms (0.4% of total)

exact: 1.0ms (0.4% of total)

ival-neg: 1.0ms (0.4% of total)

adjust: 0.0ms (0% of total)

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

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

series47.0ms (0.5%)

Memory

-17.2MiB live, 72.9MiB allocated; 11ms collecting garbage

Counts

27 → 143

Calls

Call 1

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

Outputs
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI)))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))) cosTheta)
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ 1 (PI))
(+ (* -2 (/ cosTheta (PI))) (/ 1 (PI)))
(+ 1 (* -1 (sqrt (/ 1 (PI)))))
(+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ 1 cosTheta)
(/ (+ 1 (* -1 cosTheta)) cosTheta)
(/ (+ 1 (* cosTheta (- (* -1/2 cosTheta) 1))) cosTheta)
(/ (+ 1 (* cosTheta (- (* cosTheta (- (* -1/2 cosTheta) 1/2)) 1))) cosTheta)
(* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ 1 cosTheta))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)))))
(/ 1 (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))) (/ 1 (+ 1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))
(- (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ cosTheta (PI))) (/ (* (exp (* -1 (pow cosTheta 2))) (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))) (* (sqrt -2) (+ 1 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 3))))))) (pow cosTheta 6))) (/ 1 (+ 1 (* (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 (* (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 (* (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 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))) 2))))))))
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(* (sqrt (/ cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))))
(* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (sqrt -2))))
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(* -2 (/ cosTheta (PI)))
(* cosTheta (- (/ 1 (* cosTheta (PI))) (* 2 (/ 1 (PI)))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ 1 cosTheta))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)))))
(* (sqrt (/ 1 cosTheta)) (sqrt -2))
(+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2)))
(+ (* -1/8 (* (sqrt (/ 1 (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ 1 cosTheta)) (sqrt -2))))
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(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))
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(/ 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 (+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))))
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(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta))))
(/ 1 (+ 1 (* -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 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))) 2))))) (/ 1 (+ 1 (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))))))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3))))))
(+ (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))) (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (+ (* -1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (* 1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))))))
(* -1 (* cosTheta (- (* 2 (/ 1 (PI))) (/ 1 (* cosTheta (PI))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (* -1 (sqrt (/ 1 (PI))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2))))
(+ (* -1 (* (sqrt (/ 1 cosTheta)) (* (sqrt -1) (sqrt 2)))) (* -1/2 (* (sqrt (/ 1 (pow cosTheta 3))) (/ (sqrt -1) (sqrt 2)))))
(+ (* -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))))))
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(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))))
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(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
1
(+ 1 c)
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
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(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))) c)
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c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (/ 1 c)))
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
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(/ (- (+ 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)
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
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(* -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))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
22.0ms	cosTheta	@	inf	((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))))
6.0ms	cosTheta	@	-inf	((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))))
3.0ms	cosTheta	@	0	((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))))
3.0ms	c	@	0	((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))))
2.0ms	c	@	inf	((* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (sqrt (+ (* (* -2 cosTheta) (PI)) (PI))) (PI)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (/ (+ (* -2 cosTheta) 1) (PI)) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))))

simplify317.0ms (3.5%)

Memory

4.5MiB live, 337.8MiB allocated; 58ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	739	6943
1	2530	6703
0	8319	6403

Stop Event

1×	iter limit
1×	node limit

Counts

143 → 142

Calls

Call 1

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

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

rewrite142.0ms (1.5%)

Memory

-7.2MiB live, 188.7MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	494
0	118	494
1	455	458
0	3977	456

Stop Event

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

Counts

27 → 404

Calls

Call 1

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

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

eval77.0ms (0.8%)

Memory: 15.3MiB live, 157.0MiB allocated; 22ms collecting garbage
Compiler: Compiled 30 646 to 2 924 computations (90.5% saved)

prune43.0ms (0.5%)

Memory

21.5MiB live, 114.3MiB allocated; 11ms collecting garbage

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	569	21	590
Fresh	14	10	24
Picked	2	3	5
Done	0	2	2
Total	585	36	621

Accuracy

99.9%

Counts

621 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.8%	(pow.f32 (pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	53.5%	(pow.f32 (.f32 (+.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32))) (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal -1/2 binary32))
✓	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	98.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (/ (+ ( -2 cosTheta) 1) (PI)) (.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32)) (/.f32 #s(literal 2 binary32) (PI.f32))) cosTheta))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) cosTheta)) cosTheta))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 (*.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta) cosTheta)) cosTheta))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	95.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))) cosTheta))))
	56.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta) cosTheta (.f32 cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (*.f32 cosTheta cosTheta)))))
	52.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) #s(approx (/ (+ (* (- (* (sqrt (/ 1 (PI))) (* -3/2 cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal -1 binary32) cosTheta) #s(literal -3/2 binary32)) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta))) cosTheta)))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	91.4%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 #s(approx (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (/.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	54.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) c #s(literal 1 binary32))))
	97.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (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) (+.f32 #s(literal 1 binary32) c))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (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))))
	55.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (.f32 (neg.f32 c) (-.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)) (neg.f32 c)) #s(literal 1 binary32)))))
▶	95.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) c)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	53.4%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
	94.8%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
✓	91.9%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
▶	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (PI.f32) cosTheta)) #s(literal 1 binary32))))
	96.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
✓	95.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	94.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	94.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (+.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))))
▶	46.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))) cosTheta))))
	46.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (.f32 (-.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta))) (*.f32 cosTheta cosTheta))) cosTheta))))
▶	91.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	52.6%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))) cosTheta)))))
	52.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
✓	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	95.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (.f32 (fma.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) (.f32 (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)))
	94.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (.f32 (fma.f32 (.f32 (PI.f32) cosTheta) (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))) cosTheta)))

Compiler

Compiled 3 743 to 2 382 computations (36.4% saved)

simplify123.0ms (1.3%)

Memory

1.5MiB live, 185.4MiB allocated; 40ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	1103
0	147	1103
1	269	1074
2	723	1067
3	2735	1023
0	8534	991

Stop Event

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

Calls

Call 1

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

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

localize300.0ms (3.3%)

Memory

17.0MiB live, 584.5MiB allocated; 81ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.29296875	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) c #s(literal 1 binary32))))
accuracy	0.3855123343514805	(.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))
accuracy	0.80078125	(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
accuracy	14.111926757030119	(fma.f32 (+.f32 #s(literal 1 binary32) (.f32 (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (*.f32 c cosTheta)) (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))))) c #s(literal 1 binary32))
accuracy	0.546875	(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))) cosTheta)
accuracy	0.6996897029924596	#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))) cosTheta))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	15.597254364610537	(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) (+.f32 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) cosTheta))) (*.f32 cosTheta cosTheta))
accuracy	0.5625	(/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) c)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.6980684627609016	#s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) c)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy	0.9975040160632626	(fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -3/2 binary32) cosTheta #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) c))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	0.546875	(/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.6996897029924596	#s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy	1.0	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	2.19554365943546	#s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))
accuracy	0.27734375	(*.f32 (PI.f32) cosTheta)
accuracy	0.28515625	(/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (PI.f32) cosTheta))
accuracy	0.296875	(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (PI.f32) cosTheta)) #s(literal 1 binary32)))
accuracy	0.34994125976844204	(fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (PI.f32) cosTheta)) #s(literal 1 binary32))

Samples

231.0ms

256×

valid

Compiler

Compiled 703 to 79 computations (88.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 193.0ms

ival-div: 62.0ms (32.1% of total)

ival-mult: 58.0ms (30% of total)

ival-add: 49.0ms (25.4% of total)

ival-sqrt: 8.0ms (4.1% of total)

ival-pow: 6.0ms (3.1% of total)

ival-exp: 4.0ms (2.1% of total)

ival-sub: 2.0ms (1% of total)

ival-pi: 1.0ms (0.5% of total)

exact: 1.0ms (0.5% of total)

ival-neg: 1.0ms (0.5% of total)

adjust: 0.0ms (0% of total)

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

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

series163.0ms (1.8%)

Memory

-49.0MiB live, 218.4MiB allocated; 62ms collecting garbage

Counts

29 → 171

Calls

Call 1

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

Outputs
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(sqrt (PI))
(+ (sqrt (PI)) (* -1 (* cosTheta (sqrt (PI)))))
(+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* -1/2 (* cosTheta (sqrt (PI)))))))
(+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* cosTheta (+ (* -1/2 (sqrt (PI))) (* -1/2 (* cosTheta (sqrt (PI)))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)
(* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))
(/ (+ cosTheta (sqrt (/ 1 (PI)))) (pow cosTheta 2))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (pow cosTheta 2))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) (pow cosTheta 2))
(* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))
(/ (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* c (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))))) (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))))) (* cosTheta (+ (* c (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))) (* c (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))))))))) cosTheta)
(/ 1 (* cosTheta (PI)))
(/ (+ (* -1 (/ (pow cosTheta 2) (PI))) (/ 1 (PI))) cosTheta)
(/ (+ (* (pow cosTheta 2) (- (* 1/2 (/ (pow cosTheta 2) (PI))) (/ 1 (PI)))) (/ 1 (PI))) cosTheta)
(/ (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ (* -1/6 (/ (pow cosTheta 2) (PI))) (* 1/2 (/ 1 (PI))))) (/ 1 (PI)))) (/ 1 (PI))) cosTheta)
(* cosTheta (PI))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
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(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
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(* (sqrt (* cosTheta (PI))) (sqrt -2))
(* cosTheta (+ (* 1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -2))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -2)))))
(* cosTheta (+ (* -1/8 (* (sqrt (/ (PI) (pow cosTheta 5))) (/ 1 (pow (sqrt -2) 3)))) (+ (* 1/16 (* (sqrt (/ (PI) (pow cosTheta 7))) (/ 1 (pow (sqrt -2) 5)))) (+ (* 1/2 (* (sqrt (/ (PI) (pow cosTheta 3))) (/ 1 (sqrt -2)))) (* (sqrt (/ (PI) cosTheta)) (sqrt -2))))))
(* -3/2 (* cosTheta (sqrt (/ 1 (PI)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ 1 cosTheta))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (/ 1 cosTheta)))))
(* -3/2 (* (pow cosTheta 2) (sqrt (/ 1 (PI)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))
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(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (/ 1 cosTheta) (/ c cosTheta)))))
(* cosTheta (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (+ (* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI)))) (+ (/ 1 cosTheta) (/ c cosTheta))))))
(/ 1 cosTheta)
(/ (+ 1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) cosTheta)
(* -3/2 (sqrt (/ 1 (PI))))
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(* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)) c) (sqrt (/ 1 (* cosTheta (PI)))))
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(/ (exp (* -1 (pow cosTheta 2))) (* cosTheta (PI)))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (/ 1 cosTheta))))
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(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
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(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) cosTheta)
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(* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
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(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
72.0ms	cosTheta	@	inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1)) (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1) (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta)) (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ 1 (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))) c) 1) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta)) (* (PI) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) (* (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (* cosTheta cosTheta)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))
28.0ms	c	@	-inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1)) (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1) (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta)) (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ 1 (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))) c) 1) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta)) (* (PI) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) (* (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (* cosTheta cosTheta)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))
17.0ms	c	@	0	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1)) (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1) (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta)) (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ 1 (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))) c) 1) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta)) (* (PI) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) (* (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (* cosTheta cosTheta)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))
16.0ms	cosTheta	@	-inf	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1)) (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1) (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta)) (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ 1 (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))) c) 1) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta)) (* (PI) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) (* (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (* cosTheta cosTheta)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))
13.0ms	cosTheta	@	0	((/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1)) (+ (* (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta))) 1) (sqrt (* (PI) (+ (* cosTheta -2) 1))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta)) (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/ 1 (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (+ (* (+ 1 (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))) c) 1) (/ (pow (exp cosTheta) (neg cosTheta)) (* (PI) cosTheta)) (* (PI) cosTheta) (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt (/ 1 (PI))) (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) (* (+ (* (sqrt (/ 1 (PI))) (+ -3/2 (/ -1 cosTheta))) (+ (/ (sqrt (/ 1 (PI))) (* cosTheta cosTheta)) (/ 1 cosTheta))) (* cosTheta cosTheta)) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))))

simplify350.0ms (3.8%)

Memory

75.3MiB live, 558.4MiB allocated; 95ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	888	7608
1	3174	7254
0	8783	6933

Stop Event

1×	iter limit
1×	node limit

Counts

171 → 170

Calls

Call 1

Inputs
(* cosTheta (sqrt (PI)))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))))))
(* cosTheta (+ (sqrt (PI)) (* -1 (* cosTheta (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* cosTheta (+ (sqrt (PI)) (* cosTheta (- (* cosTheta (- (* -1 (* cosTheta (+ (* -1 (* (sqrt (PI)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (* (+ 1 (* -1 (sqrt (/ 1 (PI))))) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))) (* (PI) (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))) (+ (* -1 (* (sqrt (pow (PI) 3)) (pow (+ 1 (* -1 (sqrt (/ 1 (PI))))) 2))) (* (PI) (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))) (* (PI) (+ 1 (* -1 (sqrt (/ 1 (PI))))))))))
(* (/ 1 cosTheta) (sqrt (/ 1 (PI))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI))))))))))))) cosTheta)
(sqrt (PI))
(+ (sqrt (PI)) (* -1 (* cosTheta (sqrt (PI)))))
(+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* -1/2 (* cosTheta (sqrt (PI)))))))
(+ (sqrt (PI)) (* cosTheta (+ (* -1 (sqrt (PI))) (* cosTheta (+ (* -1/2 (sqrt (PI))) (* -1/2 (* cosTheta (sqrt (PI)))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(sqrt (/ 1 (PI)))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (+ (* -1/2 (sqrt (/ 1 (PI)))) (* cosTheta (+ (sqrt (/ 1 (PI))) (* -1/2 (sqrt (/ 1 (PI)))))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))) cosTheta)
(* (/ 1 (pow cosTheta 2)) (sqrt (/ 1 (PI))))
(/ (+ cosTheta (sqrt (/ 1 (PI)))) (pow cosTheta 2))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI))))))) (pow cosTheta 2))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))) (pow cosTheta 2))
(* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI))))
(/ (+ (* -1 (* (/ cosTheta c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))))))) (* (/ 1 c) (sqrt (/ 1 (PI))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI)))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* c (* cosTheta (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI)))))))) (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))))))))) cosTheta)
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* c (+ 1 (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))))) (* cosTheta (+ (* c (* cosTheta (+ (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* (/ 1 c) (sqrt (/ 1 (PI))))))) (* c (+ (* -1 (* (/ 1 c) (sqrt (/ 1 (PI))))) (* -1/2 (* (/ 1 c) (sqrt (/ 1 (PI))))))))))))) cosTheta)
(/ 1 (* cosTheta (PI)))
(/ (+ (* -1 (/ (pow cosTheta 2) (PI))) (/ 1 (PI))) cosTheta)
(/ (+ (* (pow cosTheta 2) (- (* 1/2 (/ (pow cosTheta 2) (PI))) (/ 1 (PI)))) (/ 1 (PI))) cosTheta)
(/ (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (+ (* -1/6 (/ (pow cosTheta 2) (PI))) (* 1/2 (/ 1 (PI))))) (/ 1 (PI)))) (/ 1 (PI))) cosTheta)
(* cosTheta (PI))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* -1 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI))))))))
(+ 1 (+ c (* -1 (sqrt (/ 1 (PI))))))
(+ 1 (+ c (+ (* -3/2 (* cosTheta (sqrt (/ 1 (PI))))) (* -1 (sqrt (/ 1 (PI)))))))
(+ (sqrt (/ 1 (PI))) (* -1 (* cosTheta (sqrt (/ 1 (PI))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ (* -1 (sqrt (/ 1 (PI)))) (* cosTheta (+ (* -1/2 (sqrt (/ 1 (PI)))) (* -1/2 (* cosTheta (sqrt (/ 1 (PI))))))))))
(/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))
(+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2)))))))
(- (+ (* -1 (/ (+ (* -1/4 (/ (* cosTheta (pow (exp (* -1 (pow cosTheta 2))) 2)) (* (PI) (* (pow (sqrt -2) 2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 3))))) (* -1/8 (* (sqrt (/ (pow cosTheta 3) (PI))) (/ (exp (* -1 (pow cosTheta 2))) (* (pow (sqrt -2) 3) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2)))))) (pow cosTheta 4))) (/ 1 (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))))) (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (exp (* -1 (pow cosTheta 2))) (* (sqrt -2) (pow (+ 1 (+ c (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (sqrt -2))))) 2))))))
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(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))))) cosTheta))))
(+ 1 (+ c (* -1 (* (sqrt (/ 1 (* cosTheta (PI)))) (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2)))))))
(+ 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 (+ 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))))))))
(+ 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)))))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (* -1 (sqrt (/ 1 (PI)))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (* cosTheta (+ (* -1 (/ (+ 1 (+ c (+ (* -1 (sqrt (/ 1 (PI)))) (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))))) cosTheta)) (* 3/2 (sqrt (/ 1 (PI)))))))
(* -1 (/ (- (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) 1) cosTheta))
(+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (- (sqrt (/ 1 (PI))) 1) cosTheta)))
(+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) 1) cosTheta)))
(* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI))))))
(+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (* -1/2 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))))
(+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (* 1/8 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI))))))))
(+ (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))) (+ (* -1/2 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (sqrt 2))) (sqrt (/ 1 (* (pow cosTheta 3) (PI)))))) (+ (* -1/16 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (pow (sqrt 2) 5))) (sqrt (/ 1 (* (pow cosTheta 7) (PI)))))) (* 1/8 (* (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (* c (pow (sqrt 2) 3))) (sqrt (/ 1 (* (pow cosTheta 5) (PI)))))))))
(+ 1 (* c (+ 1 (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))))))
(+ 1 (+ (* -1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (* (exp (* -1 (pow cosTheta 2))) (sqrt -1)) (sqrt 2)))) (* c (+ 1 (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI))))))))))
(+ 1 (+ (* -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)))) (* c (+ 1 (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI)))))))))))
(+ 1 (+ (* -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)))) (* c (+ 1 (* -1 (* (/ (* (exp (* -1 (pow cosTheta 2))) (* (sqrt -1) (sqrt 2))) c) (sqrt (/ 1 (* cosTheta (PI))))))))))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (+ (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI))))) (* -1 (+ 1 (* -1 (sqrt (/ 1 (PI))))))) cosTheta))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (- (sqrt (/ 1 (PI))) 1) cosTheta))))
(* (pow cosTheta 2) (+ (* -3/2 (sqrt (/ 1 (PI)))) (* -1 (/ (- (+ (sqrt (/ 1 (PI))) (* -1 (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) 1) cosTheta))))
(* -1 (* (sqrt (/ cosTheta (PI))) (* (sqrt -1) (sqrt 2))))
(* -1 (* cosTheta (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* cosTheta (+ (* -1/8 (* (sqrt (/ 1 (* (pow cosTheta 5) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (* (pow cosTheta 7) (PI)))) (/ (sqrt -1) (pow (sqrt 2) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (* (pow cosTheta 3) (PI)))) (/ (sqrt -1) (sqrt 2)))) (* (sqrt (/ 1 (* cosTheta (PI)))) (* (sqrt -1) (sqrt 2))))))))
(/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (* c (- (* c (+ (* -1 (/ c (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 4))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3)))) (/ 1 (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)))) (/ 1 (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))))
(+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(+ (sqrt (/ 1 (PI))) (+ (* c cosTheta) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))))
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))))
(/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) cosTheta)
(+ c (+ (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))) (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))))
(* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))
(+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))))
(+ 1 (+ c (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))))
(+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))
(+ 1 (+ c (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))
(/ 1 c)
(/ (+ 1 (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c))) c)
(/ (- (+ 1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))) c)
(/ (- (+ 1 (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) (pow c 3)))) (+ (* -1 (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) (pow c 2))) (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)))) c)
(* c cosTheta)
(* c (+ cosTheta (+ (* (/ 1 c) (sqrt (/ 1 (PI)))) (/ (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)))) c))))
c
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ 1 (* c cosTheta)) (sqrt (/ 1 (PI)))) (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c)))))
(* c (+ 1 (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI)))) (/ 1 c))))
(* c (+ 1 (+ (* (/ (- (* -3/2 cosTheta) 1) c) (sqrt (/ 1 (PI)))) (/ 1 c))))
(* -1 (/ (- (+ (* (/ (exp (* -1 (pow cosTheta 2))) (* c cosTheta)) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))) (/ 1 c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2) c) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 3) c) (pow (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) 2)) c)) (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI)))))) c)) 1) c))
(* -1 (* c (+ (* -1 cosTheta) (* -1 (/ (+ (sqrt (/ 1 (PI))) (* cosTheta (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))))) c)))))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (- 1 (* 2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (+ (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1)) (* (/ 1 cosTheta) (sqrt (/ 1 (PI)))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (/ (exp (* -1 (pow cosTheta 2))) cosTheta) (sqrt (/ (+ 1 (* -2 cosTheta)) (PI))))) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ 1 (* (sqrt (/ 1 (PI))) (- (* -3/2 cosTheta) 1))) c)) 1)))

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

rewrite346.0ms (3.8%)

Memory

-48.2MiB live, 298.7MiB allocated; 149ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	918
0	147	918
1	596	821
0	4988	803

Stop Event

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

Counts

29 → 346

Calls

Call 1

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

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

eval79.0ms (0.9%)

Memory: 19.8MiB live, 167.9MiB allocated; 25ms collecting garbage
Compiler: Compiled 43 742 to 3 609 computations (91.7% saved)

prune71.0ms (0.8%)

Memory

-25.4MiB live, 167.6MiB allocated; 14ms collecting garbage

Pruning

31 alts after pruning (26 fresh and 5 done)

	Pruned	Kept	Total
New	568	10	578
Fresh	10	16	26
Picked	4	1	5
Done	1	4	5
Total	583	31	614

Accuracy

99.9%

Counts

614 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.8%	(pow.f32 (pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	53.5%	(pow.f32 (.f32 (+.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32))) (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal -1/2 binary32))
✓	98.5%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta) cosTheta)) cosTheta))))
	94.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	90.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	96.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))) cosTheta))))
	97.8%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	49.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (exp (* (neg cosTheta) cosTheta)))) (fma.f32 (+.f32 #s(literal 1 binary32) #s(approx (* (/ (exp (* (neg cosTheta) cosTheta)) (* c cosTheta)) (sqrt (/ (+ (* -2 cosTheta) 1) (PI)))) (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta c)))) c #s(literal 1 binary32))))
	97.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (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) (+.f32 #s(literal 1 binary32) c))))
	97.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (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))))
	52.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta c)) (/.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) c)) (/.f32 #s(literal 1 binary32) c)) c c))))
	95.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (+.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (*.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) c))))
	53.4%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) (+ 1 c)) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (neg.f32 c) (-.f32 (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (-.f32 (.f32 #s(literal -3/2 binary32) cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32))))))
	53.4%	(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 #s(literal -3/2 binary32) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))))
	94.8%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) cosTheta) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (sqrt.f32 (PI.f32))) cosTheta))
✓	91.9%	#s(approx (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	97.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 (sqrt.f32 (fma.f32 (*.f32 #s(literal -2 binary32) cosTheta) (PI.f32) (PI.f32))) (PI.f32)) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32))))
	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(approx (/ (pow (exp cosTheta) (neg cosTheta)) ( (PI) cosTheta)) (/.f32 (fma.f32 (-.f32 (.f32 (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (PI.f32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) #s(literal 1 binary32))))
	98.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(approx (/ (pow (exp cosTheta) (neg cosTheta)) ( (PI) cosTheta)) (/.f32 (fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta)) #s(literal 1 binary32))))
	97.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(approx (/ (pow (exp cosTheta) (neg cosTheta)) ( (PI) cosTheta)) (/.f32 (/.f32 (fma.f32 (neg.f32 cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) cosTheta)) #s(literal 1 binary32))))
	95.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(approx (/ (pow (exp cosTheta) (neg cosTheta)) ( (PI) cosTheta)) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (PI.f32))) #s(literal 1 binary32))))
	98.3%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 cosTheta #s(literal -2 binary32) #s(literal 1 binary32)))) #s(approx (/ (pow (exp cosTheta) (neg cosTheta)) ( (PI) cosTheta)) (/.f32 (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (.f32 cosTheta (PI.f32)))) #s(literal 1 binary32))))
	96.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 cosTheta #s(literal 1/2 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	94.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (+.f32 cosTheta (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))))
	46.4%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -3/2 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(approx (+ (/ (sqrt (/ 1 (PI))) ( cosTheta cosTheta)) (/ 1 cosTheta)) (/.f32 (+.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))) cosTheta))))
✓	91.2%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 #s(approx (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	52.5%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) #s(approx (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) #s(approx (/ (+ (* (+ (* (sqrt (/ 1 (PI))) (+ (* -3/2 cosTheta) -1)) 1) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (neg.f32 cosTheta) (fma.f32 #s(literal 3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) cosTheta)) #s(literal 1 binary32)) (neg.f32 cosTheta))))))))
✓	4.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	95.9%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (.f32 (fma.f32 (fma.f32 (neg.f32 cosTheta) (fma.f32 (neg.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) #s(literal 2 binary32)) (.f32 (.f32 #s(literal -3/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) (.f32 (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32))) cosTheta (sqrt.f32 (PI.f32))) cosTheta)))
	94.7%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) #s(approx (/ 1 (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1)) (.f32 (fma.f32 (.f32 (PI.f32) cosTheta) (+.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (sqrt.f32 (PI.f32))) cosTheta)))

Compiler

Compiled 5 676 to 1 648 computations (71% saved)

regimes160.0ms (1.7%)

Memory

41.7MiB live, 269.8MiB allocated; 24ms collecting garbage

Counts

76 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

55.0ms	c
24.0ms	(/.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)))))
22.0ms	(+.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))))
21.0ms	cosTheta
18.0ms	(.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
98.5%	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)))`
98.5%	1	`(+.f32 #s(literal 1 binary32) c)`
98.5%	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))))`
98.5%	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)))))`
98.5%	1	`cosTheta`
98.5%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes123.0ms (1.3%)

Memory

-30.9MiB live, 162.7MiB allocated; 70ms collecting garbage

Counts

50 → 1

Calls

Call 1

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

Calls

6 calls:

46.0ms	c
17.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
17.0ms	cosTheta
15.0ms	(+.f32 #s(literal 1 binary32) c)
12.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes92.0ms (1%)

Memory

22.7MiB live, 123.1MiB allocated; 14ms collecting garbage

Counts

41 → 1

Calls

Call 1

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

Calls

6 calls:

38.0ms	c
13.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
10.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
10.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes115.0ms (1.3%)

Memory

6.8MiB live, 141.9MiB allocated; 13ms collecting garbage

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

50.0ms	c
25.0ms	(+.f32 #s(literal 1 binary32) c)
11.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
9.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
9.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 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
98.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
98.0%	1	`(+.f32 #s(literal 1 binary32) c)`
98.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
98.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
98.0%	1	`cosTheta`
98.0%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes86.0ms (0.9%)

Memory

5.1MiB live, 184.9MiB allocated; 24ms collecting garbage

Counts

29 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

40.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
11.0ms	c
10.0ms	cosTheta
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
7.0ms	(+.f32 #s(literal 1 binary32) c)

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes34.0ms (0.4%)

Memory

-6.5MiB live, 100.3MiB allocated; 8ms collecting garbage

Counts

17 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
6.0ms	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	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
95.8%	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	`(.f32 (.f32 (/.f32 #s(literal 1 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	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes29.0ms (0.3%)

Memory

18.8MiB live, 65.0MiB allocated; 3ms collecting garbage

Counts

16 → 1

Calls

Call 1

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

Outputs

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

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)))
5.0ms	c
5.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
5.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.0%	1	`(+.f32 #s(literal 1 binary32) c)`
95.0%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
95.0%	1	`cosTheta`
95.0%	1	`c`
95.0%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
95.0%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes76.0ms (0.8%)

Memory

-0.9MiB live, 45.7MiB allocated; 2ms collecting garbage

Counts

15 → 1

Calls

Call 1

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

Calls

6 calls:

54.0ms	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 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
4.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
4.0ms	c

Results

Accuracy	Segments	Branch
94.8%	1	`c`
94.8%	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)))`
94.8%	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))))`
94.8%	1	`(+.f32 #s(literal 1 binary32) c)`
94.8%	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)))))`
94.8%	1	`cosTheta`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes46.0ms (0.5%)

Memory

-30.1MiB live, 28.5MiB allocated; 11ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

Calls

6 calls:

32.0ms	cosTheta
3.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
3.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
3.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	c

Results

Accuracy	Segments	Branch
94.7%	1	`c`
94.7%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
94.7%	1	`(+.f32 #s(literal 1 binary32) c)`
94.7%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
94.7%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
94.7%	1	`cosTheta`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes23.0ms (0.2%)

Memory

-14.3MiB live, 31.7MiB allocated; 2ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

6 calls:

10.0ms	(+.f32 #s(literal 1 binary32) c)
2.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
2.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
2.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
2.0ms	c

Results

Accuracy	Segments	Branch
91.9%	1	`c`
91.9%	1	`(+.f32 #s(literal 1 binary32) c)`
91.9%	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)))`
91.9%	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))))`
91.9%	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)))))`
91.9%	1	`cosTheta`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes7.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
4.9%	1	`c`
4.9%	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)))`
4.9%	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))))`
4.9%	1	`(+.f32 #s(literal 1 binary32) c)`
4.9%	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)))))`
4.9%	1	`cosTheta`

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify64.0ms (0.7%)

Memory

6.8MiB live, 50.7MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	553
1	216	535
2	507	525
3	1658	522
4	7530	522

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations1.1s (12.1%)

Memory

30.8MiB live, 1 313.1MiB allocated; 228ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	888	7608
1	3174	7254
0	8783	6933
0	75	494
0	118	494
1	455	458
0	3977	456
0	378	2856
1	1220	2772
2	5849	2705
0	8690	2591
0	18	66
0	33	66
1	133	59
0	1016	58
0	739	6943
1	2530	6703
0	8319	6403
0	60	447
0	100	447
1	364	379
2	2737	379
0	8191	379
0	652	6136
1	2221	5922
0	8591	5687

Stop Event

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

Compiler

Compiled 553 to 134 computations (75.8% saved)

preprocess59.0ms (0.6%)

Memory: -0.3MiB live, 89.4MiB allocated; 13ms collecting garbage
Compiler: Compiled 1 156 to 304 computations (73.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze30.0ms (0.3%)

sample2.3s (24.6%)

explain245.0ms (2.7%)

preprocess164.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify150.0ms (1.6%)

localize47.0ms (0.5%)

series27.0ms (0.3%)

simplify182.0ms (2%)

rewrite103.0ms (1.1%)

eval17.0ms (0.2%)

prune13.0ms (0.1%)

simplify257.0ms (2.8%)

localize165.0ms (1.8%)

series68.0ms (0.7%)

simplify320.0ms (3.5%)

rewrite248.0ms (2.7%)

eval166.0ms (1.8%)

prune68.0ms (0.7%)

simplify229.0ms (2.5%)

localize341.0ms (3.7%)

series47.0ms (0.5%)

simplify317.0ms (3.5%)

rewrite142.0ms (1.5%)

eval77.0ms (0.8%)

prune43.0ms (0.5%)

simplify123.0ms (1.3%)

localize300.0ms (3.3%)

series163.0ms (1.8%)

simplify350.0ms (3.8%)

rewrite346.0ms (3.8%)

eval79.0ms (0.9%)

prune71.0ms (0.8%)

regimes160.0ms (1.7%)

regimes123.0ms (1.3%)

regimes92.0ms (1%)

regimes115.0ms (1.3%)

regimes86.0ms (0.9%)

regimes34.0ms (0.4%)

regimes29.0ms (0.3%)

regimes76.0ms (0.8%)

regimes46.0ms (0.5%)

regimes23.0ms (0.2%)

regimes7.0ms (0.1%)

simplify64.0ms (0.7%)

derivations1.1s (12.1%)

preprocess59.0ms (0.6%)

end0.0ms (0%)

Profiling