Metrics for Beckmann Sample, normalization factor

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze43.0ms (0.4%)

Memory

-40.3MiB live, 56.9MiB allocated; 21ms 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)

sample2.4s (24.5%)

Memory

70.9MiB live, 3 662.6MiB allocated; 740ms collecting garbage

Samples

1.8s	8 256×	0	valid
9.0ms	62×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-div: 265.0ms (18.5% of total)

ival-<: 219.0ms (15.3% of total)

ival-mult: 183.0ms (12.8% of total)

ival-sub: 166.0ms (11.6% of total)

const: 166.0ms (11.6% of total)

ival-sqrt: 127.0ms (8.9% of total)

ival-exp: 92.0ms (6.4% of total)

ival-add: 91.0ms (6.4% of total)

ival-neg: 41.0ms (2.9% of total)

ival-pi: 36.0ms (2.5% of total)

ival-and: 24.0ms (1.7% of total)

exact: 14.0ms (1% of total)

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

adjust: 3.0ms (0.2% of total)

Bogosity

explain331.0ms (3.4%)

Memory

36.3MiB live, 501.9MiB allocated; 44ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f32`	`(/.f32 #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)))))`	n/o	1	0
↳	`(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)`	overflow	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)))`	overflow	1
↳	`(*.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta))`	overflow	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))))`	overflow	1

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

69.0ms

512×

valid

Compiler

Compiled 281 to 58 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-div: 12.0ms (24.5% of total)

ival-mult: 8.0ms (16.3% of total)

ival-sqrt: 6.0ms (12.2% of total)

ival-pi: 5.0ms (10.2% of total)

ival-add: 5.0ms (10.2% of total)

ival-sub: 5.0ms (10.2% of total)

ival-exp: 4.0ms (8.2% of total)

ival-neg: 2.0ms (4.1% 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)

preprocess237.0ms (2.5%)

Memory

-55.5MiB live, 238.0MiB allocated; 85ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Compiler

Compiled 25 to 18 computations (28% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB 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)

simplify127.0ms (1.3%)

Memory

16.9MiB live, 205.5MiB allocated; 27ms 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)

localize64.0ms (0.7%)

Memory

-18.8MiB live, 71.7MiB allocated; 11ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.09375	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.3434175597866236	(/.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	0.5709762695368841	(*.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

52.0ms

256×

valid

Compiler

Compiled 128 to 20 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 26.0ms (60.5% of total)

ival-mult: 4.0ms (9.3% of total)

ival-add: 3.0ms (7% of total)

ival-sqrt: 3.0ms (7% of total)

ival-exp: 2.0ms (4.7% of total)

ival-sub: 2.0ms (4.7% of total)

ival-pi: 1.0ms (2.3% of total)

ival-neg: 1.0ms (2.3% 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)

series29.0ms (0.3%)

Memory

-15.8MiB live, 27.9MiB allocated; 11ms collecting garbage

Counts

5 → 52

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	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))))

simplify194.0ms (2%)

Memory

50.0MiB live, 230.0MiB allocated; 50ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	443	3914
1	1311	3731
2	6026	3665
0	8212	3475

Stop Event

1×	iter limit
1×	node limit

Counts

52 → 52

Calls

Call 1

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

rewrite128.0ms (1.3%)

Memory

-37.8MiB live, 107.4MiB allocated; 44ms 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)))))

eval16.0ms (0.2%)

Memory: 42.8MiB live, 42.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 5 954 to 827 computations (86.1% saved)

prune18.0ms (0.2%)

Memory

-5.3MiB live, 38.5MiB allocated; 9ms collecting garbage

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	103	18	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	18	122

Accuracy

99.5%

Counts

122 → 18

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) (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))))))
	98.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.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)))))
▶	98.2%	(/.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)))))
▶	98.3%	(/.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)))))
	97.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	92.2%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) #s(literal 1 binary32))) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.9%	(/.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 (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))))
	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (-.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))))
▶	95.0%	(/.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 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	92.1%	(/.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	97.7%	(*.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)))
	56.6%	(.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))))))
	90.2%	(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)))
	97.3%	#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 (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))))
▶	4.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))
	97.1%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (.f32 (fma.f32 (-.f32 (.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 #s(literal -3/2 binary32) (PI.f32)))) (neg.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))
	93.4%	#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 1 332 to 862 computations (35.3% saved)

simplify283.0ms (2.9%)

Memory

12.6MiB live, 345.0MiB allocated; 87ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
cost-diff	0	(+.f32 (+.f32 #s(literal 1 binary32) c) (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)))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (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))))))
cost-diff	17	(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))))
cost-diff	0	(+.f32 #s(literal 1 binary32) c)
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 (/.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 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (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 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
cost-diff	1	(fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))
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 #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 (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: 2 (0.0ms)

Iter	Nodes	Cost
0	55	586
0	91	537
1	171	529
2	492	511
3	1698	511
0	8684	511

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

localize193.0ms (2%)

Memory

-37.2MiB live, 411.8MiB allocated; 51ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.09375	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.3434175597866236	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (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))))))
accuracy	0.41796875	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	11.888419917905827	(.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)))
accuracy	0.04296875	(sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta))
accuracy	0.09375	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.3434175597866236	(/.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	0.41796875	(/.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
accuracy	0.3434175597866236	(/.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 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
accuracy	0.5703125	(/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.8990980404094633	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (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	30.452682956638114	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
accuracy	0.09375	(-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)
accuracy	0.23828125	(/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3434175597866236	(/.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	0.3828125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Samples

103.0ms

256×

valid

Compiler

Compiled 554 to 45 computations (91.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-div: 37.0ms (44.7% of total)

ival-mult: 15.0ms (18.1% of total)

ival-add: 8.0ms (9.7% of total)

ival-pi: 7.0ms (8.5% of total)

ival-sqrt: 5.0ms (6% of total)

ival-cosh: 4.0ms (4.8% of total)

ival-exp: 2.0ms (2.4% of total)

ival-sub: 2.0ms (2.4% of total)

ival-sinh: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% 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)

series121.0ms (1.3%)

Memory

15.8MiB live, 153.9MiB allocated; 25ms collecting garbage

Counts

24 → 276

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

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

6 calls:

Time	Variable		Point	Expression
47.0ms	cosTheta	@	-inf	((* (/ (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 c) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/ 1 c) (+ (* -1 cosTheta) 1) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (* (/ (/ (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)))) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (- (- 1 cosTheta) cosTheta) (sqrt (/ 1 (PI))) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sqrt (- (- 1 cosTheta) cosTheta)) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))
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simplify263.0ms (2.7%)

Memory

1.7MiB live, 372.8MiB allocated; 70ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1129	25587
1	3261	22511
0	8120	21370

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

rewrite275.0ms (2.9%)

Memory

-13.7MiB live, 323.2MiB allocated; 71ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	442
0	91	394
1	346	376
2	2559	346
0	8276	339

Stop Event

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

Counts

24 → 1 195

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

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

eval214.0ms (2.2%)

Memory: 39.3MiB live, 321.3MiB allocated; 37ms collecting garbage
Compiler: Compiled 56 052 to 4 724 computations (91.6% saved)

prune89.0ms (0.9%)

Memory

-37.6MiB live, 225.6MiB allocated; 55ms collecting garbage

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	1 005	27	1 032
Fresh	9	4	13
Picked	4	1	5
Done	0	0	0
Total	1 018	32	1 050

Accuracy

99.9%

Counts

1 050 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.0%	(pow.f32 (pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	54.1%	(pow.f32 (.f32 (+.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 c #s(literal -1 binary32))) (+.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 c #s(literal -1 binary32)))) #s(literal -1/2 binary32))
	95.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (/.f32 (fma.f32 (.f32 (sinh.f32 (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 (cosh.f32 (*.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)))) (PI.f32))))
	96.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	92.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
▶	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	92.8%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
▶	95.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	95.2%	(/.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 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal -3/2 binary32))) cosTheta))))
	95.0%	(/.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 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	94.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	92.1%	(/.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 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) cosTheta))))
	95.1%	(/.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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
	95.1%	(/.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 (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))))))
	92.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 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)))))
	95.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (fma.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	96.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	51.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (+.f32 (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 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)) #s(literal 1 binary32)) c)))
	92.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))))
▶	52.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (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 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))))
	97.7%	(*.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)))
	53.9%	(.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 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 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 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta)))))
	90.2%	(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)))
	87.8%	(exp.f32 (.f32 (log1p.f32 (+.f32 #s(approx ( (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) c)) #s(literal -1 binary32)))
▶	93.4%	#s(approx (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	4.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))

Compiler

Compiled 2 803 to 1 691 computations (39.7% saved)

simplify198.0ms (2.1%)

Memory

2.0MiB live, 282.5MiB allocated; 27ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	749
0	100	677
1	194	620
2	560	620
3	2047	598
0	8260	598

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

localize136.0ms (1.4%)

Memory

-3.1MiB live, 284.7MiB allocated; 30ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.3434175597866236	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (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 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))))
accuracy	0.5631637695368841	(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	0.8125	(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))
accuracy	15.161210342906397	(*.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 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))
accuracy	0.23828125	(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3434175597866236	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.3828125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	1.9461781465357566	#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32))
accuracy	0.3434175597866236	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
accuracy	0.5703125	(/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.8990980404094633	#s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.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	(sqrt.f32 (PI.f32))
accuracy	0.0	(PI.f32)
accuracy	0.3828125	(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
accuracy	1.800700527654645	#s(approx (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
accuracy	0.04296875	(sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))
accuracy	0.23828125	(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3434175597866236	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.3828125	(*.f32 cosTheta (sqrt.f32 (PI.f32)))

Samples

95.0ms

256×

valid

Compiler

Compiled 628 to 49 computations (92.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 18.0ms (25.2% of total)

ival-div: 17.0ms (23.8% of total)

ival-add: 10.0ms (14% of total)

ival-sqrt: 6.0ms (8.4% of total)

ival-pow: 6.0ms (8.4% of total)

ival-exp: 4.0ms (5.6% of total)

ival-cosh: 3.0ms (4.2% of total)

ival-sub: 3.0ms (4.2% of total)

ival-neg: 2.0ms (2.8% of total)

ival-pi: 1.0ms (1.4% of total)

ival-sinh: 1.0ms (1.4% 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)

series183.0ms (1.9%)

Memory

31.3MiB live, 270.9MiB allocated; 55ms collecting garbage

Counts

28 → 197

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
69.0ms	c	@	inf	((* (/ (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 c) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (/ (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)))) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (neg c) (- (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) 1)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ 1 (PI))) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1))
52.0ms	c	@	0	((* (/ (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 c) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (/ (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)))) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (neg c) (- (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) 1)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ 1 (PI))) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1))
18.0ms	c	@	-inf	((* (/ (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 c) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (/ (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)))) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (neg c) (- (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) 1)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ 1 (PI))) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1))
16.0ms	cosTheta	@	inf	((* (/ (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 c) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (/ (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)))) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (neg c) (- (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) 1)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ 1 (PI))) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1))
9.0ms	cosTheta	@	-inf	((* (/ (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 c) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (* (sqrt (PI)) cosTheta) (sqrt (PI)) (PI) (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (/ (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)))) (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (* (neg c) (- (/ (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) 1)) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (- (- 1 cosTheta) cosTheta)) (sqrt (/ 1 (PI))) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (+ (* (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1))

simplify343.0ms (3.6%)

Memory

-9.0MiB live, 413.2MiB allocated; 47ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1185	18967
1	3730	16937
0	9149	16049

Stop Event

1×	iter limit
1×	node limit

Counts

197 → 197

Calls

Call 1

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

rewrite229.0ms (2.4%)

Memory

20.4MiB live, 162.2MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	626
0	100	524
1	400	483
2	3400	483
0	8132	479

Stop Event

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

Counts

28 → 431

Calls

Call 1

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

Outputs
(.f32 (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (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 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (sqrt.f32 (PI.f32))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta))
(*.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (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 (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 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))
(.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (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 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (neg.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta)) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (neg.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(literal 1 binary32)) (pow.f32 (exp.f32 cosTheta) cosTheta))
(/.f32 (neg.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (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) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta)) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (.f32 #s(literal 1 binary32) (neg.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (.f32 #s(literal 1 binary32) (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (.f32 (pow.f32 (exp.f32 cosTheta) cosTheta) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))
(/.f32 (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta) #s(literal 1 binary32)) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (.f32 (neg.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) #s(literal 1 binary32)) (.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) #s(literal 1 binary32)) (.f32 (*.f32 (sqrt.f32 (PI.f32)) cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))
(/.f32 (.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))
(fma.f32 (cosh.f32 (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (.f32 (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(fma.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (cosh.f32 (.f32 cosTheta cosTheta)) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (sinh.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
(+.f32 (.f32 (cosh.f32 (.f32 cosTheta cosTheta)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (.f32 (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta)) (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta))))
(+.f32 (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (cosh.f32 (.f32 cosTheta cosTheta))) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (sinh.f32 (.f32 (neg.f32 cosTheta) cosTheta))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal 3 binary32)) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 3 binary32)))) (fma.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))) (-.f32 c #s(literal -1 binary32))) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32))))
(.f32 (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
(.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))))
(pow.f32 (exp.f32 (log1p.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) c))) #s(literal -1 binary32))
(pow.f32 (.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal -1/2 binary32))
(pow.f32 (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))))) #s(literal -1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal 1 binary32))
(pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1 binary32))
(+.f32 (cosh.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) #s(literal -1 binary32))) (sinh.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) #s(literal -1 binary32))))
(exp.f32 (+.f32 #s(literal 0 binary32) (.f32 (log1p.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) #s(literal -1 binary32))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) c)) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32)))))
(neg.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))))))
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(/.f32 (-.f32 (pow.f32 (neg.f32 (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) cosTheta)) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) #s(literal 2 binary32))) (-.f32 (neg.f32 (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) cosTheta)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)))
(/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (/.f32 (neg.f32 cosTheta) cosTheta) #s(literal 3 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) #s(literal 3 binary32))) (+.f32 (pow.f32 (neg.f32 (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) cosTheta)) #s(literal 2 binary32)) (-.f32 (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) #s(literal 2 binary32)) (*.f32 (neg.f32 (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) cosTheta)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta)))))
(/.f32 (neg.f32 (neg.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (fma.f32 (neg.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32)))) cosTheta (/.f32 cosTheta (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta))
(/.f32 (-.f32 (pow.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (-.f32 (neg.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32)))) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))
(/.f32 (fma.f32 (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32)) (pow.f32 (PI.f32) #s(literal -3/2 binary32))) (.f32 (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 cosTheta cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (*.f32 (neg.f32 cosTheta) (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta))
(/.f32 (neg.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) (neg.f32 cosTheta))
(/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (neg.f32 cosTheta) cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
(fma.f32 (neg.f32 cosTheta) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 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) (neg.f32 (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) cosTheta)))
(+.f32 (neg.f32 (/.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32))) cosTheta)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
(neg.f32 (/.f32 (neg.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32)))) cosTheta))
(neg.f32 (/.f32 (*.f32 (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (neg.f32 cosTheta)))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (neg.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (neg.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)))) (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (neg.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (neg.f32 (sqrt.f32 (PI.f32)))))
(*.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)))
(sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (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 (exp.f32 (log.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)))) #s(literal 1/2 binary32))
(pow.f32 (*.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))) #s(literal 1/4 binary32))
(pow.f32 (pow.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 (pow.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(literal 1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(literal 1/2 binary32))
(+.f32 (cosh.f32 (.f32 (log.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1/2 binary32))) (sinh.f32 (.f32 (log.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1/2 binary32))))
(exp.f32 (-.f32 (.f32 (log1p.f32 (.f32 #s(literal -2 binary32) cosTheta)) #s(literal 1/2 binary32)) (log.f32 (sqrt.f32 (PI.f32)))))
(exp.f32 (*.f32 (log.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) #s(literal 1/2 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.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) (neg.f32 cosTheta))) #s(literal 2 binary32))) (-.f32 #s(literal 1 binary32) (.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)))))
(/.f32 (neg.f32 (expm1.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) cosTheta (log.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta))) #s(literal 2 binary32)))) (neg.f32 (fma.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))) #s(literal -1 binary32))))
(/.f32 (neg.f32 (-.f32 (pow.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) (neg.f32 cosTheta))) #s(literal 3 binary32)) #s(literal -1 binary32))) (neg.f32 (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 2 binary32)) (pow.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 (/.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)))))))
(/.f32 (expm1.f32 (*.f32 (fma.f32 (neg.f32 cosTheta) cosTheta (log.f32 (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta))) #s(literal 2 binary32))) (fma.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))) #s(literal -1 binary32)))
(/.f32 (-.f32 (pow.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) (neg.f32 cosTheta))) #s(literal 3 binary32)) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (pow.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) (neg.f32 cosTheta))) #s(literal 2 binary32)) (*.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))))))
(/.f32 (-.f32 (pow.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) (neg.f32 cosTheta))) #s(literal 3 binary32)) #s(literal -1 binary32)) (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 2 binary32)) (pow.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 (/.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))))))
(-.f32 (/.f32 (pow.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) (neg.f32 cosTheta))) #s(literal 2 binary32)) (fma.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))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.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))) #s(literal -1 binary32))))
(-.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) (neg.f32 cosTheta))) #s(literal -1 binary32))
(-.f32 #s(literal 1 binary32) (*.f32 (neg.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 #s(literal 1 binary32) (*.f32 (neg.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)))
(fma.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 (neg.f32 cosTheta) #s(literal 2 binary32)))) (pow.f32 (exp.f32 cosTheta) (/.f32 (neg.f32 cosTheta) #s(literal 2 binary32))) #s(literal 1 binary32))
(fma.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)) #s(literal 1 binary32))
(fma.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))) #s(literal 1 binary32))
(fma.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)) #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 (*.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))) #s(literal 1 binary32) #s(literal 1 binary32))
(fma.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)) #s(literal 1 binary32))
(fma.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (/.f32 (sqrt.f32 (/.f32 (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)) (PI.f32))) cosTheta) #s(literal 1 binary32))
(fma.f32 #s(literal 1 binary32) (*.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))) #s(literal 1 binary32))
(+.f32 (/.f32 (pow.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) (neg.f32 cosTheta))) #s(literal 3 binary32)) (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 2 binary32)) (pow.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 (/.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)))))) (/.f32 #s(literal 1 binary32) (fma.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 2 binary32)) (pow.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 (/.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)))))))
(+.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) (neg.f32 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))) cosTheta) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))))

eval187.0ms (2%)

Memory: -27.4MiB live, 216.0MiB allocated; 46ms collecting garbage
Compiler: Compiled 46 927 to 3 544 computations (92.4% saved)

prune82.0ms (0.9%)

Memory

7.6MiB live, 152.7MiB allocated; 11ms collecting garbage

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	703	12	715
Fresh	11	15	26
Picked	2	3	5
Done	0	1	1
Total	716	31	747

Accuracy

100.0%

Counts

747 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.7%	(pow.f32 (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.0%	(pow.f32 (pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	92.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) #s(literal 1 binary32)) cosTheta) (sqrt.f32 (PI.f32))) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
▶	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
▶	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	60.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (neg.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32)))) cosTheta (/.f32 cosTheta (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta)))))
	94.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) cosTheta)) cosTheta))))
	92.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	95.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
	95.0%	(/.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 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
▶	94.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	95.1%	(/.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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
▶	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	94.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	95.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (fma.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	96.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	51.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (+.f32 (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 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)) #s(literal 1 binary32)) c)))
▶	92.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))))
✓	52.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (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 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))))
	51.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 (/.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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)) (neg.f32 c)) #s(literal 1 binary32)))))
	50.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 (/.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) 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)) (neg.f32 c)) #s(literal 1 binary32)))))
	47.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 (/.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))) (neg.f32 c)) #s(literal 1 binary32)))))
	49.5%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 #s(approx (/ (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (neg c)) (/.f32 (fma.f32 (/.f32 #s(literal -1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (*.f32 (fma.f32 (/.f32 #s(literal -1 binary32) c) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) c)) (neg.f32 cosTheta))) cosTheta)) #s(literal 1 binary32)))))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 3/2 binary32)) cosTheta))
✓	93.4%	#s(approx (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	4.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))

Compiler

Compiled 3 137 to 1 828 computations (41.7% saved)

simplify153.0ms (1.6%)

Memory

-16.1MiB live, 267.4MiB allocated; 19ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	857
0	114	797
1	212	741
2	604	721
3	2416	717
0	8381	709

Stop Event

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

Calls

Call 1

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

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

localize176.0ms (1.8%)

Memory

-4.6MiB live, 378.1MiB allocated; 53ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.23828125	(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3395113097866236	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.37890625	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	0.6685859514906934	#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (fma.f32 #s(literal -1 binary32) cosTheta #s(literal 1 binary32)))
accuracy	0.32995304839252004	#s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy	0.3395113097866236	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
accuracy	0.55859375	(/.f32 (fma.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.9921875	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	0.34375000000524847	(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta)
accuracy	0.5703125	(/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)
accuracy	0.7563260726089617	#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))
accuracy	0.9921875	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	0.3395113097866236	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))))
accuracy	0.565448779305326	(*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))
accuracy	0.9921875	(sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	1.6379947193885944	#s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))
accuracy	0.23828125	(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 cosTheta (sqrt.f32 (PI.f32))))
accuracy	0.3395113097866236	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
accuracy	0.37890625	(*.f32 cosTheta (sqrt.f32 (PI.f32)))
accuracy	2.2735919708606476	#s(approx (+ 1 c) #s(literal 1 binary32))

Samples

107.0ms	254×	0	valid
3.0ms	2×	5	exit

Compiler

Compiled 640 to 56 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-mult: 31.0ms (37.3% of total)

ival-div: 20.0ms (24.1% of total)

ival-add: 10.0ms (12% of total)

ival-cosh: 5.0ms (6% of total)

ival-sqrt: 5.0ms (6% of total)

ival-sub: 3.0ms (3.6% of total)

ival-exp: 2.0ms (2.4% of total)

ival-neg: 2.0ms (2.4% of total)

adjust: 1.0ms (1.2% of total)

ival-pi: 1.0ms (1.2% of total)

exact: 1.0ms (1.2% of total)

ival-sinh: 1.0ms (1.2% of total)

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

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

series59.0ms (0.6%)

Memory

36.5MiB live, 89.5MiB allocated; 6ms collecting garbage

Counts

25 → 208

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
23.0ms	c	@	0	((+ (+ 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))) (* (sqrt (/ 1 (PI))) (/ 1 cosTheta)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (sqrt (/ 1 (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* -1 cosTheta) 1) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (* (- (/ 1 cosTheta) 1) cosTheta) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))
7.0ms	cosTheta	@	-inf	((+ (+ 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))) (* (sqrt (/ 1 (PI))) (/ 1 cosTheta)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (sqrt (/ 1 (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* -1 cosTheta) 1) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (* (- (/ 1 cosTheta) 1) cosTheta) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))
6.0ms	cosTheta	@	inf	((+ (+ 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))) (* (sqrt (/ 1 (PI))) (/ 1 cosTheta)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (sqrt (/ 1 (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* -1 cosTheta) 1) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (* (- (/ 1 cosTheta) 1) cosTheta) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))
4.0ms	cosTheta	@	0	((+ (+ 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))) (* (sqrt (/ 1 (PI))) (/ 1 cosTheta)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (sqrt (/ 1 (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* -1 cosTheta) 1) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (* (- (/ 1 cosTheta) 1) cosTheta) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))
2.0ms	c	@	-inf	((+ (+ 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))) (* (sqrt (/ 1 (PI))) (/ 1 cosTheta)) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (sqrt (/ 1 (PI))) (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta)))) (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (+ (* -1 cosTheta) 1) (/ 1 (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))))) (* cosTheta (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (/ (* (+ (* -1 cosTheta) 1) (sqrt (/ 1 (PI)))) cosTheta) (* (- (/ 1 cosTheta) 1) cosTheta) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (sqrt (- (- 1 cosTheta) cosTheta)) (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))))

simplify274.0ms (2.9%)

Memory

3.3MiB live, 429.9MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1061	20331
1	3202	17231
0	8116	16628

Stop Event

1×	iter limit
1×	node limit

Counts

208 → 208

Calls

Call 1

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

rewrite245.0ms (2.6%)

Memory

-25.7MiB live, 260.3MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	653
0	114	568
1	433	507
2	3411	507
0	8221	496

Stop Event

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

Counts

25 → 363

Calls

Call 1

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

Outputs
(.f32 (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal 1/2 binary32)) (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal 1/2 binary32)))
(.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal 1 binary32))
(/.f32 (-.f32 (pow.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal 2 binary32)) (pow.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(approx (+ 1 c) #s(literal 1 binary32))))
(/.f32 (-.f32 (pow.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) #s(literal 3 binary32))) (fma.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (+ 1 c) #s(literal 1 binary32)) (+.f32 (pow.f32 (.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta))) #s(literal 2 binary32)) (.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))))))
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(+.f32 (neg.f32 cosTheta) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (neg.f32 cosTheta))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32)) (pow.f32 (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) #s(literal 2 binary32)))) (-.f32 (-.f32 c #s(literal -1 binary32)) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) #s(literal 3 binary32)) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 3 binary32)))) (fma.f32 (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 c #s(literal -1 binary32))) (pow.f32 (-.f32 c #s(literal -1 binary32)) #s(literal 2 binary32))))
(.f32 (pow.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) (pow.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)))
(.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32)))))
(/.f32 #s(literal -1 binary32) (neg.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))))))
(/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))))
(pow.f32 (exp.f32 (log1p.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c))) #s(literal -1 binary32))
(pow.f32 (.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))) (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal -1/2 binary32))
(pow.f32 (pow.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (neg.f32 (neg.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))))) #s(literal -1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32)))) #s(literal 1 binary32))
(pow.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))) #s(literal -1 binary32))
(+.f32 (cosh.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c)) #s(literal -1 binary32))) (sinh.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c)) #s(literal -1 binary32))))
(exp.f32 (+.f32 #s(literal 0 binary32) (.f32 (log1p.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c)) #s(literal -1 binary32))))
(exp.f32 (.f32 (log1p.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) c)) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32)))))
(neg.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (-.f32 c #s(literal -1 binary32))))))
(*.f32 (sqrt.f32 (PI.f32)) cosTheta)
(*.f32 cosTheta (sqrt.f32 (PI.f32)))
(/.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (neg.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (neg.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))))) (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (neg.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32))))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)))
(.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)) (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta))
(.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)) cosTheta))
(/.f32 (/.f32 (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta))) #s(literal -1 binary32)) cosTheta)
(/.f32 (/.f32 (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta))) cosTheta) #s(literal -1 binary32))
(/.f32 (neg.f32 (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)))) (neg.f32 (neg.f32 cosTheta)))
(/.f32 (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta))) (neg.f32 cosTheta))
(/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta)
(neg.f32 (/.f32 (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32))) #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta))) cosTheta))
(neg.f32 (/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)) (pow.f32 (PI.f32) #s(literal -1/2 binary32))) (neg.f32 cosTheta)))
(*.f32 (expm1.f32 (neg.f32 (log.f32 cosTheta))) cosTheta)
(*.f32 cosTheta (expm1.f32 (neg.f32 (log.f32 cosTheta))))
(/.f32 (*.f32 (-.f32 (pow.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/.f32 (*.f32 (-.f32 (pow.f32 cosTheta #s(literal -3 binary32)) #s(literal 1 binary32)) cosTheta) (+.f32 (+.f32 (pow.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)))
(/.f32 (*.f32 cosTheta (-.f32 (pow.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32))) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))
(/.f32 (*.f32 cosTheta (-.f32 (pow.f32 cosTheta #s(literal -3 binary32)) #s(literal 1 binary32))) (+.f32 (+.f32 (pow.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) cosTheta)))
#s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.f32 (fma.f32 (/.f32 #s(literal -3/2 binary32) (sqrt.f32 (PI.f32))) cosTheta (/.f32 #s(literal -1 binary32) (sqrt.f32 (PI.f32)))) cosTheta (pow.f32 (PI.f32) #s(literal -1/2 binary32))) cosTheta))
#s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (sqrt.f32 (PI.f32))) cosTheta)
(/.f32 (neg.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta)) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (neg.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)))) (neg.f32 (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))
(/.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) cosTheta) (sqrt.f32 (PI.f32)))
(/.f32 (neg.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta))) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
(neg.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (*.f32 (neg.f32 cosTheta) (sqrt.f32 (PI.f32)))))

eval124.0ms (1.3%)

Memory: 22.9MiB live, 169.8MiB allocated; 12ms collecting garbage
Compiler: Compiled 46 115 to 3 291 computations (92.9% saved)

prune70.0ms (0.7%)

Memory

-5.0MiB live, 167.5MiB allocated; 30ms collecting garbage

Pruning

35 alts after pruning (28 fresh and 7 done)

	Pruned	Kept	Total
New	694	11	705
Fresh	5	17	22
Picked	2	3	5
Done	0	4	4
Total	701	35	736

Accuracy

100.0%

Counts

736 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(pow.f32 (pow.f32 (fma.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) #s(approx (+ 1 c) #s(literal 1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	95.0%	(pow.f32 (pow.f32 (+.f32 #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (*.f32 (/.f32 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) cosTheta) (-.f32 #s(literal 1 binary32) cosTheta))) (-.f32 c #s(literal -1 binary32))) #s(literal -1/2 binary32)) #s(literal 2 binary32))
	97.7%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 (/.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta) (PI.f32))) cosTheta) (exp.f32 (.f32 (neg.f32 cosTheta) cosTheta)))))
✓	98.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (/.f32 #s(approx (sqrt (- (- 1 cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) cosTheta)) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
✓	96.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) cosTheta (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	60.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (neg.f32 (/.f32 cosTheta (sqrt.f32 (PI.f32)))) cosTheta (/.f32 cosTheta (sqrt.f32 (PI.f32)))) (*.f32 cosTheta cosTheta)))))
	94.9%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (.f32 (.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta))) cosTheta)) cosTheta))))
	92.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 #s(approx (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	54.0%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -3/2 binary32)) (.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))))) cosTheta)))))
	54.3%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (+ (* (* (sqrt (/ 1 (PI))) -3/2) cosTheta) (neg (sqrt (/ 1 (PI))))) cosTheta) (sqrt (/ 1 (PI)))) cosTheta) (.f32 (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 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32))) (neg.f32 cosTheta))) (neg.f32 cosTheta))))))
	95.1%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) #s(approx (/ (+ (* (sqrt (/ 1 (PI))) (neg cosTheta)) (sqrt (/ 1 (PI)))) cosTheta) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) cosTheta)))))))
	95.0%	(/.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 (*.f32 (-.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) 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))) (/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (/.f32 (*.f32 (-.f32 (pow.f32 cosTheta #s(literal -2 binary32)) #s(literal 1 binary32)) cosTheta) (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal -1 binary32)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
✓	94.6%	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) #s(approx (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))) (/.f32 (.f32 #s(approx (+ ( -1 cosTheta) 1) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) cosTheta) #s(literal 1 binary32)) cosTheta)) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	95.1%	(/.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 (pow.f32 (PI.f32) #s(literal -1/2 binary32)) (/.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)))))
✓	97.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) (.f32 (/.f32 (sqrt.f32 #s(approx (- (- 1 cosTheta) cosTheta) (fma.f32 #s(literal -2 binary32) cosTheta #s(literal 1 binary32)))) (.f32 cosTheta (sqrt.f32 (PI.f32)))) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
	94.9%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))) (/.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (neg.f32 cosTheta) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	96.6%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (/.f32 (fma.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))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta))))
	96.1%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #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))))
	92.2%	(/.f32 #s(literal 1 binary32) (+.f32 #s(approx (+ 1 c) #s(literal 1 binary32)) #s(approx (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta))) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta)))))
	95.0%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (fma.f32 #s(literal -1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) c) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	96.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (fma.f32 (+.f32 (+.f32 #s(literal 1 binary32) c) (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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)))))) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	92.8%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 (/.f32 #s(literal 1 binary32) cosTheta) (sqrt.f32 (PI.f32)))))
	92.9%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))))
	51.6%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (+.f32 (fma.f32 (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 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)) #s(literal 1 binary32)) c)))
✓	52.1%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (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 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) cosTheta) #s(literal 1 binary32)) (neg.f32 c)) #s(literal 1 binary32)))))
	51.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 (/.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32) (.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)) (neg.f32 c)) #s(literal 1 binary32)))))
	50.7%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 (/.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (/.f32 (fma.f32 (+.f32 (fma.f32 (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) #s(literal -3/2 binary32)) 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)) (neg.f32 c)) #s(literal 1 binary32)))))
	47.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta))))) (.f32 (neg.f32 c) (-.f32 (/.f32 #s(approx (+ ( (sqrt (/ (+ (* -2 cosTheta) 1) (PI))) (/ (pow (exp cosTheta) (neg cosTheta)) cosTheta)) 1) (*.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) cosTheta))) (neg.f32 c)) #s(literal 1 binary32)))))
	96.3%	(/.f32 #s(literal 1 binary32) #s(approx (+ (+ 1 c) (* (/ (sqrt (- (- 1 cosTheta) cosTheta)) (* cosTheta (sqrt (PI)))) (exp (* (neg cosTheta) cosTheta)))) (/.f32 (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)) c) #s(literal 1 binary32)) cosTheta (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) cosTheta)))
	93.4%	#s(approx (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 3/2 binary32)) cosTheta))
✓	93.4%	#s(approx (/ 1 (+ (+ 1 c) (+ (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (cosh (* cosTheta cosTheta))) (* (/ (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta) (sqrt (PI))) (sinh (* (neg cosTheta) cosTheta)))))) (*.f32 (sqrt.f32 (PI.f32)) cosTheta))
✓	4.8%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (/.f32 #s(literal 1 binary32) c))
	96.0%	#s(approx (/ 1 (+ (+ 1 c) (* (* (/ 1 (sqrt (PI))) (/ (sqrt (- (- 1 cosTheta) cosTheta)) cosTheta)) (exp (* (neg cosTheta) cosTheta))))) (*.f32 (fma.f32 (fma.f32 (-.f32 c (sqrt.f32 (/.f32 #s(literal 1 binary32) (PI.f32)))) (PI.f32) (PI.f32)) (neg.f32 cosTheta) (sqrt.f32 (PI.f32))) cosTheta))

Compiler

Compiled 5 110 to 1 572 computations (69.2% saved)

regimes218.0ms (2.3%)

Memory

5.3MiB live, 388.9MiB allocated; 137ms collecting garbage

Counts

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

56.0ms	(+.f32 #s(literal 1 binary32) c)
36.0ms	cosTheta
35.0ms	(.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)))
35.0ms	(/.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)))))
32.0ms	c

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	`(/.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`
98.3%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes75.0ms (0.8%)

Memory

13.4MiB live, 207.6MiB allocated; 14ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

14.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
14.0ms	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))))
12.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
11.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.3%	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	`(/.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`
98.3%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes75.0ms (0.8%)

Memory

8.5MiB live, 196.3MiB allocated; 15ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

14.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
13.0ms	cosTheta
12.0ms	c
11.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
11.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
97.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
97.9%	1	`(+.f32 #s(literal 1 binary32) c)`
97.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
97.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
97.9%	1	`cosTheta`
97.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes776.0ms (8.1%)

Memory

-167.8MiB live, 191.4MiB allocated; 1.1s collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

720.0ms	cosTheta
13.0ms	c
11.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Results

Accuracy	Segments	Branch
97.7%	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)))`
97.7%	1	`(+.f32 #s(literal 1 binary32) c)`
97.7%	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))))`
97.7%	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)))))`
97.7%	1	`cosTheta`
97.7%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes129.0ms (1.3%)

Memory

-30.2MiB live, 68.7MiB allocated; 42ms collecting garbage

Counts

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

Outputs

(/.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))))

Calls

6 calls:

61.0ms	cosTheta
27.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
10.0ms	c
10.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
10.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))

Results

Accuracy	Segments	Branch
96.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.9%	1	`cosTheta`
96.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.9%	1	`(+.f32 #s(literal 1 binary32) c)`
96.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes66.0ms (0.7%)

Memory

17.8MiB live, 65.1MiB allocated; 8ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

24.0ms	cosTheta
9.0ms	c
8.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
8.0ms	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
8.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
96.9%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.9%	1	`cosTheta`
96.9%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.9%	1	`(+.f32 #s(literal 1 binary32) c)`
96.9%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.9%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes58.0ms (0.6%)

Memory

2.7MiB live, 147.6MiB allocated; 13ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
96.6%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
96.6%	1	`(+.f32 #s(literal 1 binary32) c)`
96.6%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
96.6%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
96.6%	1	`cosTheta`
96.6%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes60.0ms (0.6%)

Memory

-10.7MiB live, 180.5MiB allocated; 13ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

13.0ms	(+.f32 #s(literal 1 binary32) c)
11.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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	cosTheta
8.0ms	c

Results

Accuracy	Segments	Branch
96.3%	1	`(+.f32 #s(literal 1 binary32) c)`
96.3%	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)))))`
96.3%	1	`cosTheta`
96.3%	1	`c`
96.3%	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)))`
96.3%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes45.0ms (0.5%)

Memory

8.9MiB live, 101.1MiB allocated; 6ms collecting garbage

Counts

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

Outputs

(/.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))))

Calls

6 calls:

9.0ms	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	c
7.0ms	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
7.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
96.3%	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)))))`
96.3%	1	`cosTheta`
96.3%	1	`(+.f32 #s(literal 1 binary32) c)`
96.3%	1	`c`
96.3%	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)))`
96.3%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes44.0ms (0.5%)

Memory

2.2MiB live, 98.3MiB allocated; 8ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
96.3%	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)))`
96.3%	1	`(+.f32 #s(literal 1 binary32) c)`
96.3%	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))))`
96.3%	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)))))`
96.3%	1	`cosTheta`
96.3%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes38.0ms (0.4%)

Memory

-4.2MiB live, 86.7MiB allocated; 6ms collecting garbage

Counts

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

Outputs

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

Calls

6 calls:

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

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes35.0ms (0.4%)

Memory

29.8MiB live, 75.1MiB allocated; 3ms collecting garbage

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

6 calls:

7.0ms	(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))
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	(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
5.0ms	c
5.0ms	cosTheta

Results

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

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes38.0ms (0.4%)

Memory

-15.0MiB live, 37.2MiB allocated; 31ms collecting garbage

Counts

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

23.0ms	c
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 #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 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))
3.0ms	cosTheta

Results

Accuracy	Segments	Branch
93.4%	1	`(.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))`
93.4%	1	`(+.f32 #s(literal 1 binary32) c)`
93.4%	1	`(+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))`
93.4%	1	`(/.f32 #s(literal 1 binary32) (+.f32 (+.f32 #s(literal 1 binary32) c) (.f32 (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 #s(literal 1 binary32) cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))`
93.4%	1	`cosTheta`
93.4%	1	`c`

Compiler

Compiled 72 to 58 computations (19.4% saved)

regimes10.0ms (0.1%)

Memory

-24.1MiB live, 22.7MiB allocated; 6ms 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:

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

Results

Accuracy	Segments	Branch
4.8%	1	`c`
4.8%	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)))))`
4.8%	1	`cosTheta`
4.8%	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)))`
4.8%	1	`(+.f32 #s(literal 1 binary32) c)`
4.8%	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))))`

Compiler

Compiled 72 to 58 computations (19.4% saved)

simplify52.0ms (0.5%)

Memory

31.1MiB live, 74.8MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	560
1	211	540
2	506	530
3	1531	530

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

derivations381.0ms (4%)

Memory

-14.2MiB live, 311.8MiB allocated; 63ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 590 to 127 computations (78.5% saved)

preprocess56.0ms (0.6%)

Memory: 41.1MiB live, 131.1MiB allocated; 13ms collecting garbage
Compiler: Compiled 1 230 to 290 computations (76.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze43.0ms (0.4%)

sample2.4s (24.5%)

explain331.0ms (3.4%)

preprocess237.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify127.0ms (1.3%)

localize64.0ms (0.7%)

series29.0ms (0.3%)

simplify194.0ms (2%)

rewrite128.0ms (1.3%)

eval16.0ms (0.2%)

prune18.0ms (0.2%)

simplify283.0ms (2.9%)

localize193.0ms (2%)

series121.0ms (1.3%)

simplify263.0ms (2.7%)

rewrite275.0ms (2.9%)

eval214.0ms (2.2%)

prune89.0ms (0.9%)

simplify198.0ms (2.1%)

localize136.0ms (1.4%)

series183.0ms (1.9%)

simplify343.0ms (3.6%)

rewrite229.0ms (2.4%)

eval187.0ms (2%)

prune82.0ms (0.9%)

simplify153.0ms (1.6%)

localize176.0ms (1.8%)

series59.0ms (0.6%)

simplify274.0ms (2.9%)

rewrite245.0ms (2.6%)

eval124.0ms (1.3%)

prune70.0ms (0.7%)

regimes218.0ms (2.3%)

regimes75.0ms (0.8%)

regimes75.0ms (0.8%)

regimes776.0ms (8.1%)

regimes129.0ms (1.3%)

regimes66.0ms (0.7%)

regimes58.0ms (0.6%)

regimes60.0ms (0.6%)

regimes45.0ms (0.5%)

regimes44.0ms (0.5%)

regimes38.0ms (0.4%)

regimes35.0ms (0.4%)

regimes38.0ms (0.4%)

regimes10.0ms (0.1%)

simplify52.0ms (0.5%)

derivations381.0ms (4%)

preprocess56.0ms (0.6%)

end0.0ms (0%)

Profiling