Metrics for GTR1 distribution

start0.0ms (0%)

Memory: 0.2MiB live, 0.1MiB allocated

analyze56.0ms (0.5%)

Memory

7.1MiB live, 124.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.6%	99.4%	0%	0%	0%	0
0%	0%	0.6%	99.4%	0%	0%	0%	1
0%	0%	0.6%	99.4%	0%	0%	0%	2
0%	0%	0.6%	99.4%	0%	0%	0%	3
0%	0%	0.6%	99.4%	0%	0%	0%	4
50%	0.3%	0.3%	99.4%	0%	0%	0%	5
50%	0.3%	0.3%	99.4%	0%	0%	0%	6
75%	0.5%	0.2%	99.4%	0%	0%	0%	7
75%	0.5%	0.2%	99.4%	0%	0%	0%	8
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	9
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	10
93.7%	0.6%	0%	99.4%	0%	0%	0%	11
93.7%	0.6%	0%	99.4%	0%	0%	0%	12

Compiler

Compiled 40 to 23 computations (42.5% saved)

sample1.8s (17.6%)

Memory

-67.7MiB live, 2 322.1MiB allocated

Samples

1.4s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-<=: 417.0ms (34.7% of total)

ival-mult: 334.0ms (27.8% of total)

const: 120.0ms (10% of total)

ival-log: 85.0ms (7.1% of total)

ival-sub: 72.0ms (6% of total)

ival-div: 62.0ms (5.2% of total)

ival-add: 40.0ms (3.3% of total)

ival-pi: 33.0ms (2.7% of total)

ival-and: 24.0ms (2% of total)

exact: 10.0ms (0.8% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain205.0ms (2%)

Memory

32.7MiB live, 265.3MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))`
-	-	`(PI.f32)`
-	-	`#s(literal 1 binary32)`
-	-	`cosTheta`
-	-	`alpha`
-	-	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
-	-	`(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))`
-	-	`(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))`
-	-	`(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)`
-	-	`(log.f32 (*.f32 alpha alpha))`
-	-	`(*.f32 alpha alpha)`
-	-	`(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)`
-	-	`(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

62.0ms

512×

valid

Compiler

Compiled 210 to 43 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 15.0ms (46.6% of total)

ival-log: 6.0ms (18.6% of total)

ival-div: 4.0ms (12.4% of total)

ival-pi: 2.0ms (6.2% of total)

ival-add: 2.0ms (6.2% of total)

ival-sub: 2.0ms (6.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess202.0ms (2%)

Memory

-28.2MiB live, 204.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 798×	`lower-fma.f64`
12 798×	`lower-fma.f32`
4 578×	`lower-*.f64`
4 568×	`lower-*.f32`
2 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	130
1	148	122
2	629	120
3	3565	120
4	7829	120
0	13	24
0	23	24
1	51	24
2	159	24
3	643	24
4	2693	24
5	4403	24
6	7704	24
0	8552	21

Stop Event

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

Calls

Call 1

Inputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))

Symmetry

(abs alpha)

(abs cosTheta)

Compiler

Compiled 24 to 13 computations (45.8% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Status

Accuracy

Program

▶

98.5%

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Compiler

Compiled 24 to 13 computations (45.8% saved)

simplify193.0ms (1.9%)

Memory

1.3MiB live, 158.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff	64	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
cost-diff	64	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))

Rules

12 798×	`lower-fma.f64`
12 798×	`lower-fma.f32`
4 578×	`lower-*.f64`
4 568×	`lower-*.f32`
2 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	91
0	23	91
1	51	91
2	159	91
3	643	91
4	2693	91
5	4403	91
6	7704	91
0	8552	81

Stop Event

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

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta

localize36.0ms (0.4%)

Memory

2.6MiB live, 75.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.16796875	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.29296875	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
accuracy	0.3671875	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

27.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 7.0ms (40.6% of total)

ival-sub: 3.0ms (17.4% of total)

ival-log: 3.0ms (17.4% of total)

ival-div: 2.0ms (11.6% of total)

ival-pi: 1.0ms (5.8% of total)

ival-add: 1.0ms (5.8% of total)

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

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

exact: 0.0ms (0% of total)

series101.0ms (1%)

Memory

-20.8MiB live, 101.4MiB allocated

Counts

7 → 132

Calls

Call 1

Inputs
#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) (patch (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) #<representation binary32>) () ())
#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())
#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (patch (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #<representation binary32>) () ())
#s(alt (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) (patch (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta) (patch (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta) #<representation binary32>) () ())

Outputs
#s(alt -1 (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* -1 (pow cosTheta 2))) (taylor 0 alpha) (#s(alt (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) (patch (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))) (taylor 0 alpha) (#s(alt (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) (patch (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))) (taylor 0 alpha) (#s(alt (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) (patch (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))) (taylor 0 alpha) (#s(alt (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) (patch (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)) #<representation binary32>) () ())) ())
#s(alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (* 2 (* (PI) (log alpha))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (patch (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #<representation binary32>) () ())) ())
#s(alt (* 2 (* (PI) (log alpha))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (patch (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #<representation binary32>) () ())) ())
#s(alt (* 2 (* (PI) (log alpha))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (patch (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #<representation binary32>) () ())) ())
#s(alt (* 2 (* (PI) (log alpha))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (patch (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #<representation binary32>) () ())) ())
#s(alt (* -1 cosTheta) (taylor 0 alpha) (#s(alt (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) (patch (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) #<representation binary32>) () ())) ())
#s(alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta)) (taylor 0 alpha) (#s(alt (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) (patch (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) #<representation binary32>) () ())) ())
#s(alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta)) (taylor 0 alpha) (#s(alt (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) (patch (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) #<representation binary32>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	alpha	@	0	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
21.0ms	alpha	@	inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
9.0ms	alpha	@	-inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
2.0ms	cosTheta	@	inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
2.0ms	cosTheta	@	0	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))

simplify193.0ms (1.9%)

Memory

18.6MiB live, 245.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
5 952×	`lower-*.f64`
5 952×	`lower-*.f32`
4 632×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	2350
1	582	2290
2	2231	2197
0	8702	2075

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* -1 (pow cosTheta 2))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))

Outputs
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (/.f32 cosTheta (log.f32 alpha)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (-.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (/.f32 cosTheta (log.f32 alpha)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))) (.f32 (.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (/.f32 cosTheta (log.f32 alpha)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))) (.f32 cosTheta cosTheta)) (/.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (/.f32 (.f32 cosTheta cosTheta) (log.f32 alpha)) (fma.f32 (.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (/.f32 cosTheta (log.f32 alpha)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* -1 (pow cosTheta 2))
(*.f32 (neg.f32 cosTheta) cosTheta)
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 (.f32 (*.f32 cosTheta cosTheta) alpha) alpha)
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))) alpha) alpha #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))) alpha) alpha #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha)))) alpha) alpha #s(literal 1 binary32))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (neg.f32 (log.f32 alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(fma.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))) (.f32 alpha alpha)) #s(literal -1/2 binary32) (+.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (neg.f32 (log.f32 alpha))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
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(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (log.f32 (.f32 alpha alpha))))) (*.f32 cosTheta cosTheta))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)

rewrite406.0ms (4%)

Memory

-3.7MiB live, 284.6MiB allocated

Rules

6 278×	`lower-*.f64`
6 268×	`lower-*.f32`
5 746×	`lower-fma.f64`
5 746×	`lower-fma.f32`
3 952×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
0	23	65
1	98	65
2	768	63
0	8446	55

Stop Event

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

Counts

7 → 609

Calls

Call 1

Inputs
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(*.f32 alpha alpha)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)

Outputs
(expm1.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (-.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) alpha))
(*.f32 (neg.f32 (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(*.f32 (+.f32 (neg.f32 alpha) #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) alpha))
(*.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(*.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
(*.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha))
(*.f32 (+.f32 #s(literal 1 binary32) alpha) (neg.f32 (-.f32 #s(literal 1 binary32) alpha)))
(*.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 alpha #s(literal 1 binary32)))
(*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))
(.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))))
(*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))) (+.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))) (+.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (*.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (*.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))))
(/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (*.f32 (neg.f32 alpha) alpha))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)))) (neg.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (neg.f32 (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)))) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 #s(literal 1 binary32) alpha)))
(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 8 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 12 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (+.f32 (pow.f32 alpha #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 4 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 12 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 18 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (+.f32 (pow.f32 alpha #s(literal 12 binary32)) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (pow.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) #s(literal 2 binary32)))
(/.f32 (-.f32 (.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) #s(literal 1 binary32))) (*.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(/.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (neg.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (*.f32 (neg.f32 alpha) alpha))))
(/.f32 (neg.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (neg.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (*.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (*.f32 (neg.f32 alpha) alpha)))
(/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (*.f32 (neg.f32 alpha) alpha)) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(-.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))))
(-.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(-.f32 (/.f32 (pow.f32 alpha #s(literal 6 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(-.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(fma.f32 (*.f32 #s(literal 1 binary32) alpha) alpha #s(literal -1 binary32))
(fma.f32 (/.f32 (pow.f32 alpha #s(literal 3 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 alpha #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (exp.f32 (log.f32 alpha)) (exp.f32 (log.f32 alpha)) #s(literal -1 binary32))
(fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (*.f32 (-.f32 alpha #s(literal 1 binary32)) alpha))
(fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (*.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32)))
(fma.f32 (+.f32 #s(literal 1 binary32) alpha) alpha (*.f32 (+.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32)))
(fma.f32 (pow.f32 alpha #s(literal 4 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (pow.f32 alpha #s(literal 6 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))))
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(fma.f32 #s(literal 1 binary32) (*.f32 alpha alpha) #s(literal -1 binary32))
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(fma.f32 (.f32 cosTheta alpha) alpha (.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 (fma.f32 alpha cosTheta cosTheta) alpha (*.f32 (fma.f32 alpha cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 1 binary32) (.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) cosTheta (.f32 (.f32 alpha alpha) cosTheta))
(fma.f32 cosTheta #s(literal -1 binary32) (.f32 cosTheta (.f32 alpha alpha)))
(fma.f32 cosTheta (.f32 alpha alpha) (.f32 (*.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 cosTheta (.f32 alpha alpha) (.f32 cosTheta #s(literal -1 binary32)))
(fma.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) cosTheta) (*.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(fma.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 alpha alpha)) (.f32 #s(literal 1 binary32) (.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta))
(fma.f32 alpha (fma.f32 alpha cosTheta cosTheta) (*.f32 #s(literal -1 binary32) (fma.f32 alpha cosTheta cosTheta)))
(+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 1 binary32)) (.f32 (neg.f32 cosTheta) #s(literal 1 binary32)))
(+.f32 (.f32 alpha (fma.f32 alpha cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (fma.f32 alpha cosTheta cosTheta)))
(+.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) cosTheta)) (.f32 #s(literal 1 binary32) (neg.f32 cosTheta)))
(+.f32 (.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 alpha alpha))) (.f32 #s(literal 1 binary32) (*.f32 cosTheta #s(literal -1 binary32))))
(+.f32 (.f32 (fma.f32 alpha cosTheta cosTheta) alpha) (.f32 (fma.f32 alpha cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (neg.f32 cosTheta) (.f32 (.f32 alpha alpha) cosTheta))
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(+.f32 (.f32 cosTheta #s(literal -1 binary32)) (.f32 cosTheta (*.f32 alpha alpha)))
(+.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (.f32 cosTheta (.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32)))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (-.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal 1 binary32) alpha))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (+.f32 #s(literal 1 binary32) alpha)) (-.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 (*.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))
(.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)
(.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta))
(.f32 #s(literal 1 binary32) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta))
(/.f32 (neg.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)) (neg.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))))
(/.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) cosTheta) cosTheta)))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta (*.f32 (neg.f32 cosTheta) cosTheta))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta (.f32 (.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(fma.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)))
(fma.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta) (.f32 (neg.f32 cosTheta) cosTheta))
(+.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) (.f32 (*.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(+.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta)) (.f32 cosTheta (neg.f32 cosTheta)))
(+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))) (.f32 cosTheta (*.f32 cosTheta #s(literal -1 binary32))))

eval464.0ms (4.5%)

Memory: 20.1MiB live, 139.7MiB allocated
Compiler: Compiled 30 076 to 2 884 computations (90.4% saved)

prune378.0ms (3.7%)

Memory

-31.5MiB live, 254.7MiB allocated

Pruning

35 alts after pruning (34 fresh and 1 done)

	Pruned	Kept	Total
New	849	34	883
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	849	35	884

Accuracy

99.5%

Counts

884 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
▶	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 alpha (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
▶	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 alpha (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (/.f32 alpha (PI.f32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (/.f32 (.f32 alpha alpha) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (.f32 (/.f32 alpha (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (/.f32 alpha (PI.f32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (.f32 (/.f32 alpha (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 alpha (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal 1 binary32) (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal 1 binary32)))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.3%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))
▶	71.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
	98.4%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	67.2%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	11.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))

Compiler

Compiled 2 146 to 1 149 computations (46.5% saved)

simplify9.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
cost-diff	0	(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
cost-diff	0	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
cost-diff	0	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
cost-diff	0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(/.f32 alpha #s(literal 1 binary32))
cost-diff	0	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff	0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
cost-diff	0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Rules

36×	`lower-*.f64`
28×	`lift-*.f32`
18×	`lift-/.f32`
18×	`lower-/.f64`
16×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	520
0	81	520

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
(log.f32 alpha)
(+.f32 (PI.f32) (PI.f32))
(PI.f32)
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
#s(literal 1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(PI.f32)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha))
(*.f32 alpha alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))
(.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))
(fma.f32 alpha cosTheta cosTheta)
cosTheta
(*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)
(-.f32 alpha #s(literal 1 binary32))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
(log.f32 alpha)
(+.f32 (PI.f32) (PI.f32))
(PI.f32)
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
cosTheta
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
#s(literal 1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(PI.f32)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha))
(*.f32 alpha alpha)
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))
(.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))
(fma.f32 alpha cosTheta cosTheta)
cosTheta
(*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)
(-.f32 alpha #s(literal 1 binary32))

localize169.0ms (1.7%)

Memory

27.9MiB live, 140.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	15.749074497758276	(fma.f32 alpha cosTheta cosTheta)
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	(*.f32 alpha alpha)
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(log.f32 alpha)
accuracy	29.98788023102775	(PI.f32)

Samples

73.0ms

256×

invalid

Compiler

Compiled 570 to 47 computations (91.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 25.0ms (46.9% of total)

ival-div: 11.0ms (20.6% of total)

ival-add: 8.0ms (15% of total)

ival-log: 5.0ms (9.4% of total)

ival-sub: 2.0ms (3.8% of total)

ival-pi: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series254.0ms (2.5%)

Memory

-22.2MiB live, 174.8MiB allocated

Counts

24 → 300

Calls

Call 1

Inputs
#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())
#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())
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#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())
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#s(alt (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (patch (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) #<representation binary32>) () ())
#s(alt (/.f32 alpha #s(literal 1 binary32)) (patch (/.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha))) (patch (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha))) #<representation binary32>) () ())
#s(alt (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (patch (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (patch (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) #<representation binary32>) () ())
#s(alt (PI.f32) (patch (PI.f32) #<representation binary32>) () ())
#s(alt (log.f32 alpha) (patch (log.f32 alpha) #<representation binary32>) () ())
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#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)) (patch (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)) #<representation binary32>) () ())
#s(alt (fma.f32 alpha cosTheta cosTheta) (patch (fma.f32 alpha cosTheta cosTheta) #<representation binary32>) () ())
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Outputs
#s(alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
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#s(alt (- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
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#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (taylor 0 alpha) (#s(alt (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) (patch (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) #<representation binary32>) () ())) ())
#s(alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))) (taylor 0 alpha) (#s(alt (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) (patch (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) #<representation binary32>) () ())) ())
#s(alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))) (taylor 0 alpha) (#s(alt (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) (patch (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) #<representation binary32>) () ())) ())
#s(alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha)))))) (taylor 0 alpha) (#s(alt (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) (patch (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))) #<representation binary32>) () ())) ())
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#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())) ())
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#s(alt (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI)))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI)))) (taylor 0 alpha) (#s(alt (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())) ())
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#s(alt alpha (taylor 0 alpha) (#s(alt (/.f32 alpha #s(literal 1 binary32)) (patch (/.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt alpha (taylor 0 alpha) (#s(alt (/.f32 alpha #s(literal 1 binary32)) (patch (/.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())) ())
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#s(alt alpha (taylor 0 alpha) (#s(alt (/.f32 alpha #s(literal 1 binary32)) (patch (/.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())) ())
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#s(alt (+ (* -1 (/ (* (pow alpha 2) (pow cosTheta 2)) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))) (/ 1 (+ 1 (* -1 (pow cosTheta 2))))) (taylor 0 alpha) (#s(alt (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (pow cosTheta 4)) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2))))) (taylor 0 alpha) (#s(alt (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (/ (* (pow alpha 2) (pow cosTheta 6)) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))) (* -1 (/ (pow cosTheta 4) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2))))) (taylor 0 alpha) (#s(alt (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())) ())
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#s(alt (* -1 (/ (- (pow alpha 2) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))))) (taylor -inf cosTheta) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) #<representation binary32>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))))) (pow cosTheta 2)) (taylor -inf cosTheta) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) #<representation binary32>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 3) (pow (- (* -1 alpha) 1) 3)))))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 3) (pow (- (* -1 alpha) 1) 3)))))))) (pow cosTheta 2)) (taylor -inf cosTheta) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) #<representation binary32>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 4) (pow (- (* -1 alpha) 1) 4)))))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (* (pow cosTheta 4) (* (- alpha 1) (- (* -1 alpha) 1))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 4) (pow (- (* -1 alpha) 1) 4))))))))) (pow cosTheta 2)) (taylor -inf cosTheta) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (taylor -inf cosTheta) (#s(alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2)))) (taylor -inf cosTheta) (#s(alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2)))) (taylor -inf cosTheta) (#s(alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2)))) (taylor -inf cosTheta) (#s(alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* cosTheta (- (* -1 alpha) 1))) (taylor -inf cosTheta) (#s(alt (fma.f32 alpha cosTheta cosTheta) (patch (fma.f32 alpha cosTheta cosTheta) #<representation binary32>) () ())) ())
#s(alt (* -1 (* cosTheta (- (* -1 alpha) 1))) (taylor -inf cosTheta) (#s(alt (fma.f32 alpha cosTheta cosTheta) (patch (fma.f32 alpha cosTheta cosTheta) #<representation binary32>) () ())) ())
#s(alt (* -1 (* cosTheta (- (* -1 alpha) 1))) (taylor -inf cosTheta) (#s(alt (fma.f32 alpha cosTheta cosTheta) (patch (fma.f32 alpha cosTheta cosTheta) #<representation binary32>) () ())) ())
#s(alt (* -1 (* cosTheta (- (* -1 alpha) 1))) (taylor -inf cosTheta) (#s(alt (fma.f32 alpha cosTheta cosTheta) (patch (fma.f32 alpha cosTheta cosTheta) #<representation binary32>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
98.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha))) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (PI) (log alpha) (* (log alpha) (+ (PI) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)) (+ (* alpha cosTheta) cosTheta) (log (* alpha alpha)))
51.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha))) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (PI) (log alpha) (* (log alpha) (+ (PI) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)) (+ (* alpha cosTheta) cosTheta) (log (* alpha alpha)))
25.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha))) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (PI) (log alpha) (* (log alpha) (+ (PI) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)) (+ (* alpha cosTheta) cosTheta) (log (* alpha alpha)))
19.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha))) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (PI) (log alpha) (* (log alpha) (+ (PI) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)) (+ (* alpha cosTheta) cosTheta) (log (* alpha alpha)))
10.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha))) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (PI) (log alpha) (* (log alpha) (+ (PI) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)) (+ (* alpha cosTheta) cosTheta) (log (* alpha alpha)))

simplify883.0ms (8.7%)

Memory

14.4MiB live, 168.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 108×	`lower-*.f64`
8 108×	`lower-*.f32`
7 066×	`lower-fma.f64`
7 066×	`lower-fma.f32`
3 552×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	630	6945
1	2131	6466
0	9040	6184

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 287

Calls

Call 1

Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
alpha
alpha
alpha
alpha
(/ 1 (+ 1 (* -1 (pow cosTheta 2))))
(+ (* -1 (/ (* (pow alpha 2) (pow cosTheta 2)) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (pow cosTheta 4)) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (/ (* (pow alpha 2) (pow cosTheta 6)) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))) (* -1 (/ (pow cosTheta 4) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (/ (* alpha (* cosTheta (+ cosTheta (* -1 cosTheta)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* alpha (- (* alpha (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (* (pow cosTheta 2) (pow (+ cosTheta (* -1 cosTheta)) 2)) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (* cosTheta (+ cosTheta (* -1 cosTheta))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
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(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* alpha (+ (* 2 (* alpha (* (pow cosTheta 2) (* (PI) (log alpha))))) (* 2 (* cosTheta (* (PI) (* (log alpha) (+ cosTheta (* -1 cosTheta)))))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* alpha (+ (* 2 (* alpha (* (pow cosTheta 2) (* (PI) (log alpha))))) (* 2 (* cosTheta (* (PI) (* (log alpha) (+ cosTheta (* -1 cosTheta)))))))))
(log alpha)
(log alpha)
(log alpha)
(log alpha)
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
cosTheta
(+ cosTheta (* alpha cosTheta))
(+ cosTheta (* alpha cosTheta))
(+ cosTheta (* alpha cosTheta))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
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(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
alpha
alpha
alpha
alpha
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
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(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (* 1/2 (/ (+ cosTheta (* -1 cosTheta)) (* alpha (* (pow cosTheta 3) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ cosTheta (* -1 cosTheta)) (* alpha (* (pow cosTheta 3) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (pow (+ cosTheta (* -1 cosTheta)) 2) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))))
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(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* cosTheta (* (PI) (* (log (/ 1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha)) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* cosTheta (* (PI) (* (log (/ 1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha)) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* alpha cosTheta)
(* alpha (+ cosTheta (/ cosTheta alpha)))
(* alpha (+ cosTheta (/ cosTheta alpha)))
(* alpha (+ cosTheta (/ cosTheta alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
(- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
alpha
alpha
alpha
alpha
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (* 1/2 (/ (+ cosTheta (* -1 cosTheta)) (* alpha (* (pow cosTheta 3) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ cosTheta (* -1 cosTheta)) 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) alpha)) (* 1/2 (/ (+ cosTheta (* -1 cosTheta)) (* (pow cosTheta 3) (* (PI) (log (/ -1 alpha))))))) alpha)) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ cosTheta (* -1 cosTheta)) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ cosTheta (* -1 cosTheta)) 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* alpha cosTheta))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ cosTheta (* -1 cosTheta))) (* alpha (* (pow cosTheta 5) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ cosTheta (* -1 cosTheta)) 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) alpha)) (* 1/2 (/ (+ cosTheta (* -1 cosTheta)) (* (pow cosTheta 3) (* (PI) (log (/ -1 alpha))))))) alpha)) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* cosTheta (* (PI) (* (log (/ -1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -1 (/ (+ (* 2 (* cosTheta (* (PI) (* (log (/ -1 alpha)) (+ cosTheta (* -1 cosTheta)))))) (* 2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) alpha))) alpha))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -1 (/ (+ (* 2 (* cosTheta (* (PI) (* (log (/ -1 alpha)) (+ cosTheta (* -1 cosTheta)))))) (* 2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) alpha))) alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* alpha cosTheta)
(* -1 (* alpha (+ (* -1 cosTheta) (* -1 (/ cosTheta alpha)))))
(* -1 (* alpha (+ (* -1 cosTheta) (* -1 (/ cosTheta alpha)))))
(* -1 (* alpha (+ (* -1 cosTheta) (* -1 (/ cosTheta alpha)))))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log alpha)))))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log alpha)))) (* 1/2 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log alpha)))))))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
1
(+ 1 (* (pow cosTheta 2) (- 1 (pow alpha 2))))
(+ 1 (* (pow cosTheta 2) (- (+ 1 (* -1 (* (pow cosTheta 2) (* (- 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (pow alpha 2))))
(+ 1 (* (pow cosTheta 2) (- (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (* (- 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))) (* (- 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (pow alpha 2))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1)))) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (+ 1 alpha) 2) (* (pow (- alpha 1) 2) (- (pow alpha 2) 1)))) (* (PI) (log (pow alpha 2)))) (/ (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (+ 1 alpha) 3) (* (pow (- alpha 1) 3) (- (pow alpha 2) 1)))) (* (PI) (log (pow alpha 2))))) (* -1 (/ (* (pow (+ 1 alpha) 2) (* (pow (- alpha 1) 2) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2))))))) (/ (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (+ 1 alpha))
(* cosTheta (+ 1 alpha))
(* cosTheta (+ 1 alpha))
(* cosTheta (+ 1 alpha))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))
(/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
(/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ (- (pow alpha 2) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 2) (pow (- alpha 1) 2)))))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 2) (pow (- alpha 1) 2)))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 2) (pow (- alpha 1) 2)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 3) (pow (- alpha 1) 3)))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 3) (pow (- alpha 1) 3)))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 2) (pow (- alpha 1) 2))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 2) (pow (- alpha 1) 2)))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 4) (pow (- alpha 1) 4)))))) (+ (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 3) (pow (- alpha 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 3) (pow (- alpha 1) 3)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 2) (pow (- alpha 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (+ 1 alpha) 4) (pow (- alpha 1) 4)))))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1)))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1)))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1)))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- alpha 1)))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (+ 1 alpha))
(* cosTheta (+ 1 alpha))
(* cosTheta (+ 1 alpha))
(* cosTheta (+ 1 alpha))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))
(/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
(/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ 1 (* (pow cosTheta 6) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))))))) (pow cosTheta 2))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* -1 (/ (- (pow alpha 2) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 3) (pow (- (* -1 alpha) 1) 3)))))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 3) (pow (- (* -1 alpha) 1) 3)))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 4) (pow (- (* -1 alpha) 1) 4)))))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (* (pow cosTheta 4) (* (- alpha 1) (- (* -1 alpha) 1))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 4) (pow (- (* -1 alpha) 1) 4))))))))) (pow cosTheta 2))
(* -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(* -1 (* cosTheta (- (* -1 alpha) 1)))

Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) #s(literal -1/2 binary32) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (/.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))))) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))))) (.f32 alpha alpha) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(.f32 (PI.f32) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(.f32 (PI.f32) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(.f32 (PI.f32) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
alpha
alpha
alpha
alpha
(/ 1 (+ 1 (* -1 (pow cosTheta 2))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(+ (* -1 (/ (* (pow alpha 2) (pow cosTheta 2)) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
(+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (pow cosTheta 4)) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(fma.f32 (-.f32 (/.f32 (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) alpha) alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3 binary32))) (/.f32 (.f32 cosTheta cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (.f32 alpha alpha) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(+ (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (/ (* (pow alpha 2) (pow cosTheta 6)) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))) (* -1 (/ (pow cosTheta 4) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(fma.f32 (fma.f32 (fma.f32 (.f32 (neg.f32 alpha) alpha) (/.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 4 binary32))) (/.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3 binary32)))) (.f32 alpha alpha) (/.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (.f32 alpha alpha) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(- (* 1/2 (/ (* alpha (* cosTheta (+ cosTheta (* -1 cosTheta)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* cosTheta (* (PI) (* (log (/ 1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* cosTheta (* (PI) (* (log (/ 1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha)) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (+ (* -2 (/ (* cosTheta (* (PI) (* (log (/ 1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha)) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))))
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(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
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(* -2 (* (PI) (log (/ 1 alpha))))
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(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
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(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
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(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
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(* alpha cosTheta)
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(* alpha (+ cosTheta (/ cosTheta alpha)))
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(* alpha (+ cosTheta (/ cosTheta alpha)))
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(* alpha (+ cosTheta (/ cosTheta alpha)))
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(* -2 (log (/ 1 alpha)))
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(* -2 (log (/ 1 alpha)))
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(* -2 (log (/ 1 alpha)))
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(* -2 (log (/ 1 alpha)))
(*.f32 #s(literal -2 binary32) (neg.f32 (log.f32 alpha)))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
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(- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
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(- (+ (* -1/2 (/ (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
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(pow alpha 2)
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(pow alpha 2)
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(pow alpha 2)
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(pow alpha 2)
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(pow alpha 2)
(*.f32 alpha alpha)
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
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(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
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(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
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(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
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(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
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(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
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alpha
alpha
alpha
alpha
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha) cosTheta) cosTheta)
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
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(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
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(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
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(* (pow alpha 2) (pow cosTheta 2))
(.f32 (.f32 (*.f32 cosTheta cosTheta) alpha) alpha)
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
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(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
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(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
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(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
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(- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* (+ cosTheta (* -1 cosTheta)) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ cosTheta (* -1 cosTheta)) 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* alpha cosTheta))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ cosTheta (* -1 cosTheta))) (* alpha (* (pow cosTheta 5) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (pow (+ cosTheta (* -1 cosTheta)) 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) alpha)) (* 1/2 (/ (+ cosTheta (* -1 cosTheta)) (* (pow cosTheta 3) (* (PI) (log (/ -1 alpha))))))) alpha)) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
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(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* cosTheta (* (PI) (* (log (/ -1 alpha)) (+ cosTheta (* -1 cosTheta))))) alpha))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -1 (/ (+ (* 2 (* cosTheta (* (PI) (* (log (/ -1 alpha)) (+ cosTheta (* -1 cosTheta)))))) (* 2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) alpha))) alpha))))
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(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -1 (/ (+ (* 2 (* cosTheta (* (PI) (* (log (/ -1 alpha)) (+ cosTheta (* -1 cosTheta)))))) (* 2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) alpha))) alpha))))
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(+ (log -1) (* -1 (log (/ -1 alpha))))
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(+ (log -1) (* -1 (log (/ -1 alpha))))
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(* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
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(* (pow alpha 2) cosTheta)
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(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
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(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
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(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
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(* alpha cosTheta)
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(* -1 (* alpha (+ (* -1 cosTheta) (* -1 (/ cosTheta alpha)))))
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(* -1 (* alpha (+ (* -1 cosTheta) (* -1 (/ cosTheta alpha)))))
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(* -1 (* alpha (+ (* -1 cosTheta) (* -1 (/ cosTheta alpha)))))
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(* -2 (log (/ -1 alpha)))
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(* -2 (log (/ -1 alpha)))
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(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(*.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)))
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(fma.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 alpha)) (*.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log alpha)))))))
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(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log alpha)))) (* 1/2 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log alpha)))))))))
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(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
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(PI)
(PI.f32)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
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1
#s(literal 1 binary32)
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1
#s(literal 1 binary32)
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(fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
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(* (PI) (log (pow alpha 2)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
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(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
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(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
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(* cosTheta (+ 1 alpha))
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(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta)
(* -1 (/ (- (pow alpha 2) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))))
(/.f32 (/.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (neg.f32 alpha) #s(literal 1 binary32))) (-.f32 alpha #s(literal 1 binary32))))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 alpha #s(literal 1 binary32)))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)))) (/.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 3) (pow (- (* -1 alpha) 1) 3)))))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 3) (pow (- (* -1 alpha) 1) 3)))))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 3 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 3 binary32)))) (-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 alpha #s(literal 1 binary32)))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32))))) (fma.f32 (/.f32 alpha (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 3 binary32))) (.f32 (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (PI.f32)))) (/.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32)))))) (.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 4) (pow (- (* -1 alpha) 1) 4)))))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2))))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (* (pow cosTheta 4) (* (- alpha 1) (- (* -1 alpha) 1))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 2) (pow (- (* -1 alpha) 1) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (pow (- alpha 1) 4) (pow (- (* -1 alpha) 1) 4))))))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 4 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 4 binary32)))) (-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32)))) (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 alpha #s(literal 1 binary32)))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32))))) (-.f32 (fma.f32 (/.f32 alpha (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32))) (.f32 (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32)))) (/.f32 alpha (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (.f32 alpha alpha) (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 4 binary32))) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 4 binary32))))) (/.f32 (-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32)))) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (/.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 2 binary32)))) (pow.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (.f32 (.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (-.f32 alpha #s(literal 1 binary32))) (pow.f32 cosTheta #s(literal 4 binary32)))))) (*.f32 cosTheta cosTheta))
(* -1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))))
(.f32 (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (neg.f32 alpha) #s(literal 1 binary32))) (-.f32 alpha #s(literal 1 binary32))))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(.f32 (fma.f32 (.f32 (neg.f32 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 alpha #s(literal 1 binary32)))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(.f32 (fma.f32 (.f32 (neg.f32 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 alpha #s(literal 1 binary32)))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (+ (* -1 (* (PI) (* (log (pow alpha 2)) (* (- alpha 1) (- (* -1 alpha) 1))))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(.f32 (fma.f32 (.f32 (neg.f32 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 alpha #s(literal 1 binary32)))) (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(*.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (neg.f32 cosTheta))
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(*.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (neg.f32 cosTheta))
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(*.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (neg.f32 cosTheta))
(* -1 (* cosTheta (- (* -1 alpha) 1)))
(*.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (neg.f32 cosTheta))

rewrite232.0ms (2.3%)

Memory

14.8MiB live, 51.4MiB allocated

Rules

36×	`lower-*.f64`
28×	`lift-*.f32`
18×	`lift-/.f32`
18×	`lower-/.f64`
16×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	307
0	81	307

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

24 → 29

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))
(PI.f32)
(log.f32 alpha)
(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(fma.f32 alpha cosTheta cosTheta)
(log.f32 (*.f32 alpha alpha))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(+.f32 (.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(+.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta))))
(PI.f32)
(log.f32 alpha)
(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(fma.f32 alpha cosTheta cosTheta)
(+.f32 (*.f32 alpha cosTheta) cosTheta)
(log.f32 (*.f32 alpha alpha))

eval1.2s (12.2%)

Memory: -22.3MiB live, 102.5MiB allocated
Compiler: Compiled 28 434 to 1 170 computations (95.9% saved)

prune163.0ms (1.6%)

Memory

-1.7MiB live, 353.4MiB allocated

Pruning

93 alts after pruning (88 fresh and 5 done)

	Pruned	Kept	Total
New	686	68	754
Fresh	9	20	29
Picked	1	4	5
Done	0	1	1
Total	696	93	789

Accuracy

99.6%

Counts

789 → 93

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
✓	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(approx ( alpha alpha) (*.f32 alpha alpha))))
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	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
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	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
▶	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (.f32 (/.f32 alpha (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (/.f32 alpha (PI.f32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.3%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))
✓	71.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	71.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 #s(approx (+ ( alpha cosTheta) cosTheta) (fma.f32 cosTheta alpha cosTheta)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	5.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.4%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	70.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))

Compiler

Compiled 6 255 to 3 482 computations (44.3% saved)

simplify9.0ms (0.1%)

Memory

17.9MiB live, 17.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
cost-diff	0	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
cost-diff	0	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
cost-diff	0	(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(/.f32 alpha #s(literal 1 binary32))
cost-diff	0	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff	64	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(/.f32 alpha #s(literal 1 binary32))
cost-diff	0	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
cost-diff	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
cost-diff	64	(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))

Rules

40×	`lower-*.f64`
38×	`lift-*.f32`
20×	`lift-/.f32`
18×	`lower-/.f64`
14×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	685
0	104	680

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))
(.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(.f32 (.f32 alpha alpha) cosTheta)
cosTheta
(neg.f32 cosTheta)
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) alpha)
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(*.f32 cosTheta cosTheta)
cosTheta
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(PI.f32)
(*.f32 alpha alpha)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 (.f32 alpha alpha) cosTheta (neg.f32 cosTheta)) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta)) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))
(+.f32 #s(literal 1 binary32) (.f32 (fma.f32 (.f32 alpha alpha) cosTheta (neg.f32 cosTheta)) cosTheta))
(.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)
(.f32 (fma.f32 (.f32 alpha alpha) cosTheta (neg.f32 cosTheta)) cosTheta)
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta))
(.f32 (.f32 alpha alpha) cosTheta)
cosTheta
(neg.f32 cosTheta)
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) alpha)
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(*.f32 cosTheta cosTheta)
cosTheta
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(PI.f32)
(*.f32 alpha alpha)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))

localize113.0ms (1.1%)

Memory

11.1MiB live, 239.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	(*.f32 alpha alpha)
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
accuracy	0	(*.f32 alpha alpha)
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	(*.f32 cosTheta cosTheta)
accuracy	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
accuracy	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(neg.f32 cosTheta)
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)

Samples

68.0ms

256×

invalid

Compiler

Compiled 710 to 42 computations (94.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 25.0ms (54.6% of total)

ival-div: 7.0ms (15.3% of total)

ival-add: 7.0ms (15.3% of total)

ival-log: 3.0ms (6.6% of total)

ival-pi: 1.0ms (2.2% of total)

ival-sub: 1.0ms (2.2% of total)

ival-neg: 1.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series67.0ms (0.7%)

Memory

-12.0MiB live, 110.8MiB allocated

Counts

28 → 288

Calls

Call 1

Inputs
#s(alt (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) (patch (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) #<representation binary32>) () ())
#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) #<representation binary32>) () ())
#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())
#s(alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())
#s(alt (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (patch (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) #<representation binary32>) () ())
#s(alt #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (patch #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (patch (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) #<representation binary32>) () ())
#s(alt (/.f32 alpha #s(literal 1 binary32)) (patch (/.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (patch (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) #<representation binary32>) () ())
#s(alt (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (patch (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (patch (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) #<representation binary32>) () ())
#s(alt (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))) (patch (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (patch (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (patch (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (PI.f32) (patch (PI.f32) #<representation binary32>) () ())
#s(alt (log.f32 (.f32 alpha alpha)) (patch (log.f32 (.f32 alpha alpha)) #<representation binary32>) () ())
#s(alt (neg.f32 cosTheta) (patch (neg.f32 cosTheta) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (patch (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) #<representation binary32>) () ())
#s(alt #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (patch #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) #<representation binary32>) () ())
#s(alt (.f32 cosTheta cosTheta) (patch (.f32 cosTheta cosTheta) #<representation binary32>) () ())
#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (patch (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)) (patch (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)) #<representation binary32>) () ())

Outputs
#s(alt (* -1 cosTheta) (taylor 0 alpha) (#s(alt (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) (patch (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) cosTheta) cosTheta) (taylor 0 alpha) (#s(alt (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) (patch (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) cosTheta) cosTheta) (taylor 0 alpha) (#s(alt (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) (patch (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) cosTheta) cosTheta) (taylor 0 alpha) (#s(alt (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) (patch (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) #<representation binary32>) () ())) ())
#s(alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (taylor 0 alpha) (#s(alt (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) (patch (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta)))) #<representation binary32>) () ())) ())
#s(alt -1 (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (patch (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt (pow alpha 2) (taylor 0 alpha) (#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())) ())
#s(alt -1 (taylor 0 alpha) (#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow alpha 2) 1) (taylor 0 alpha) (#s(alt (fma.f32 alpha alpha #s(literal -1 binary32)) (patch (fma.f32 alpha alpha #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (taylor 0 alpha) (#s(alt #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (patch #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (patch (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (patch (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (patch (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* cosTheta (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#s(alt (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (patch (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #<representation binary32>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	alpha	@	0	((+ (* (* alpha alpha) cosTheta) (neg cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* (* alpha alpha) cosTheta) (neg cosTheta)) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (neg cosTheta) (/ 0 0) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)))
9.0ms	alpha	@	-inf	((+ (* (* alpha alpha) cosTheta) (neg cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* (* alpha alpha) cosTheta) (neg cosTheta)) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (neg cosTheta) (/ 0 0) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)))
8.0ms	alpha	@	inf	((+ (* (* alpha alpha) cosTheta) (neg cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* (* alpha alpha) cosTheta) (neg cosTheta)) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (neg cosTheta) (/ 0 0) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)))
4.0ms	cosTheta	@	-inf	((+ (* (* alpha alpha) cosTheta) (neg cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* (* alpha alpha) cosTheta) (neg cosTheta)) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (neg cosTheta) (/ 0 0) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)))
2.0ms	cosTheta	@	inf	((+ (* (* alpha alpha) cosTheta) (neg cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* (* alpha alpha) cosTheta) (neg cosTheta)) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (neg cosTheta) (/ 0 0) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (* (/ 0 0) (PI)))

simplify173.0ms (1.7%)

Memory

16.0MiB live, 282.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 200×	`lower-fma.f64`
7 200×	`lower-fma.f32`
5 398×	`lower-*.f64`
5 398×	`lower-*.f32`
3 184×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	332	4438
1	1008	4235
2	3836	4201
0	8526	3931

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 276

Calls

Call 1

Inputs
(* -1 cosTheta)
(- (* (pow alpha 2) cosTheta) cosTheta)
(- (* (pow alpha 2) cosTheta) cosTheta)
(- (* (pow alpha 2) cosTheta) cosTheta)
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
alpha
alpha
alpha
alpha
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(/ 1 (+ 1 (* -1 (pow cosTheta 2))))
(+ (* -1 (/ (* (pow alpha 2) (pow cosTheta 2)) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (pow cosTheta 4)) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (/ (* (pow alpha 2) (pow cosTheta 6)) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))) (* -1 (/ (pow cosTheta 4) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
alpha
alpha
alpha
alpha
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
alpha
alpha
alpha
alpha
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
1
(+ 1 (* (pow cosTheta 2) (- 1 (pow alpha 2))))
(+ 1 (* (pow cosTheta 2) (- (+ 1 (* -1 (* (pow cosTheta 2) (* (- 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (pow alpha 2))))
(+ 1 (* (pow cosTheta 2) (- (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (* (- 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))) (* (- 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (pow alpha 2))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(* -1 (/ (- (pow alpha 2) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2)))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 3))))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 3))))))) (pow cosTheta 2))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 4))))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2)))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (* (pow cosTheta 4) (+ 1 (* -1 (pow alpha 2)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 4)))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))

Outputs
(* -1 cosTheta)
(neg.f32 cosTheta)
(- (* (pow alpha 2) cosTheta) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(- (* (pow alpha 2) cosTheta) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(- (* (pow alpha 2) cosTheta) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (-.f32 (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 alpha alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (fma.f32 (-.f32 (.f32 (.f32 (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (.f32 alpha alpha)) (.f32 (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 alpha alpha) (fma.f32 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (PI.f32))) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) #s(literal 1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
alpha
alpha
alpha
alpha
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(- (pow alpha 2) 1)
(fma.f32 alpha alpha #s(literal -1 binary32))
(/ 1 (+ 1 (* -1 (pow cosTheta 2))))
(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
(+ (* -1 (/ (* (pow alpha 2) (pow cosTheta 2)) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta) (pow.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
(+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (pow cosTheta 4)) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(fma.f32 (fma.f32 (neg.f32 cosTheta) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) alpha) alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3 binary32)))) (.f32 alpha alpha) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(+ (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (/ (* (pow alpha 2) (pow cosTheta 6)) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))) (* -1 (/ (pow cosTheta 4) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(fma.f32 (fma.f32 (-.f32 (/.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 3 binary32))) (/.f32 (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) alpha) alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 4 binary32)))) (.f32 alpha alpha) (.f32 (neg.f32 cosTheta) (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))))) (.f32 alpha alpha) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (neg.f32 (log.f32 alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(+.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))) (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha))) (-.f32 (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))) (fma.f32 (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (+.f32 (fma.f32 (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (.f32 (neg.f32 (PI.f32)) (log.f32 alpha)))) (/.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha)))) (fma.f32 (fma.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
alpha
alpha
alpha
alpha
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 alpha alpha))) (.f32 alpha alpha))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))) (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 alpha alpha)))) (*.f32 alpha alpha))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
(/.f32 (-.f32 (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (pow.f32 alpha #s(literal 6 binary32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (pow.f32 cosTheta #s(literal 4 binary32))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)))) (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32)))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (.f32 alpha alpha)))) (*.f32 alpha alpha))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta)
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 alpha alpha) (fma.f32 (/.f32 (neg.f32 cosTheta) alpha) (/.f32 cosTheta alpha) (.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 alpha alpha) (fma.f32 (/.f32 (neg.f32 cosTheta) alpha) (/.f32 cosTheta alpha) (.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 (.f32 alpha alpha) (fma.f32 (/.f32 (neg.f32 cosTheta) alpha) (/.f32 cosTheta alpha) (.f32 cosTheta cosTheta)) #s(literal 1 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (fma.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(-.f32 (-.f32 (fma.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 alpha alpha)))) (fma.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(.f32 (.f32 (PI.f32) (fma.f32 cosTheta cosTheta (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha))) (.f32 alpha alpha))
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(PI)
(PI.f32)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
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1
#s(literal 1 binary32)
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#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
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(* -1 cosTheta)
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(* -1 cosTheta)
(neg.f32 cosTheta)
(PI)
(PI.f32)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
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(pow cosTheta 2)
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(pow cosTheta 2)
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(* cosTheta (- (pow alpha 2) 1))
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(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
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(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
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(* cosTheta (- (pow alpha 2) 1))
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(* cosTheta (- (pow alpha 2) 1))
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(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
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(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
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(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
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(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
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(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
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(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* -1 cosTheta)
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(* -1 cosTheta)
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(* -1 cosTheta)
(neg.f32 cosTheta)
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
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(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
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(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (* cosTheta (+ 1 (* -1 (pow alpha 2)))))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* -1 (/ (- (pow alpha 2) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (*.f32 cosTheta cosTheta)))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2)))))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2)))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (log.f32 (.f32 alpha alpha))) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 3))))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ (pow alpha 2) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 3))))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 4 binary32))) (PI.f32)) (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 3 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (fma.f32 (/.f32 alpha (.f32 (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (log.f32 (.f32 alpha alpha)))) (/.f32 alpha (.f32 cosTheta cosTheta)) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 3 binary32)) (log.f32 (.f32 alpha alpha))))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (* -1 (/ (- (pow alpha 2) 1) (* (PI) (* (log (pow alpha 2)) (+ 1 (* -1 (pow alpha 2))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 4))))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2)))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (* (pow cosTheta 4) (+ 1 (* -1 (pow alpha 2)))))) (+ (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 2))))) (/ (pow alpha 2) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (+ 1 (* -1 (pow alpha 2))) 4)))))))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 cosTheta #s(literal 6 binary32))) (PI.f32)) (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 4 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))))) (fma.f32 (/.f32 alpha (.f32 (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (log.f32 (.f32 alpha alpha)))) (/.f32 alpha (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32))) (/.f32 alpha (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 4 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (log.f32 (.f32 alpha alpha))))) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (pow.f32 cosTheta #s(literal 4 binary32))))))) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32))) (pow.f32 cosTheta #s(literal 6 binary32)))) (.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* -1 cosTheta)
(neg.f32 cosTheta)
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)

rewrite23.0ms (0.2%)

Memory

-1.5MiB live, 37.7MiB allocated

Rules

40×	`lower-*.f64`
38×	`lift-*.f32`
20×	`lift-/.f32`
18×	`lower-/.f64`
14×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	387
0	104	385

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

28 → 35

Calls

Call 1

Inputs
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(neg.f32 cosTheta)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
(*.f32 cosTheta cosTheta)
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))

Outputs
(fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta))
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 (.f32 alpha alpha) cosTheta (neg.f32 cosTheta)) cosTheta))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(+.f32 (.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(+.f32 (.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(+.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(neg.f32 cosTheta)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
(*.f32 cosTheta cosTheta)
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))

eval53.0ms (0.5%)

Memory: 2.0MiB live, 120.1MiB allocated
Compiler: Compiled 23 769 to 722 computations (97% saved)

prune173.0ms (1.7%)

Memory

-32.3MiB live, 428.0MiB allocated

Pruning

131 alts after pruning (123 fresh and 8 done)

	Pruned	Kept	Total
New	567	46	613
Fresh	6	77	83
Picked	1	4	5
Done	1	4	5
Total	575	131	706

Accuracy

99.6%

Counts

706 → 131

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32)))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
▶	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(approx ( alpha alpha) (*.f32 alpha alpha))))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
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✓	71.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	71.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 #s(approx (+ ( alpha cosTheta) cosTheta) (fma.f32 cosTheta alpha cosTheta)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	5.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.4%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	70.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
▶	-0.0%	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))

Compiler

Compiled 9 008 to 5 063 computations (43.8% saved)

simplify10.0ms (0.1%)

Memory

19.4MiB live, 19.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
cost-diff	0	(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
cost-diff	0	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
cost-diff	0	(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(/.f32 alpha #s(literal 1 binary32))
cost-diff	0	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff	64	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(/.f32 alpha #s(literal 1 binary32))
cost-diff	0	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
cost-diff	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
cost-diff	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
cost-diff	0	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(pow.f32 alpha #s(literal 4 binary32))
cost-diff	0	(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
cost-diff	0	(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
cost-diff	0	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Rules

52×	`lower-*.f64`
50×	`lift-*.f32`
26×	`lift-/.f32`
26×	`lower-/.f64`
12×	`lift-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	849
0	131	849

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

Inputs
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
#s(literal 1 binary32)
(pow.f32 alpha #s(literal 4 binary32))
alpha
#s(literal 4 binary32)
(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
#s(literal -1 binary32)
(*.f32 alpha alpha)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
#s(literal -1 binary32)
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) alpha)
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(*.f32 cosTheta cosTheta)
cosTheta
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta)))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))
(.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(*.f32 alpha alpha)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
cosTheta
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(*.f32 alpha alpha)
#s(literal -1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(PI.f32)
(*.f32 alpha alpha)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)

Outputs
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
#s(literal 1 binary32)
(pow.f32 alpha #s(literal 4 binary32))
alpha
#s(literal 4 binary32)
(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
#s(literal -1 binary32)
(*.f32 alpha alpha)
(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
#s(literal -1 binary32)
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
(.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)
(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) alpha)
(.f32 (.f32 cosTheta cosTheta) (PI.f32))
(*.f32 cosTheta cosTheta)
cosTheta
(PI.f32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(literal -1 binary32)
(.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta)))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))
(.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(*.f32 alpha alpha)
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
alpha
#s(literal 1 binary32)
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(PI.f32)
(fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
(*.f32 alpha alpha)
#s(literal -1 binary32)
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
#s(literal 1 binary32)
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
cosTheta
(fma.f32 alpha alpha #s(literal -1 binary32))
alpha
#s(literal -1 binary32)
(*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))
(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
#s(literal 0 binary32)
(PI.f32)
(*.f32 alpha alpha)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))
(/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)

localize137.0ms (1.3%)

Memory

5.0MiB live, 201.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	(*.f32 alpha alpha)
accuracy	0	#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
accuracy	0	(*.f32 alpha alpha)
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(*.f32 alpha alpha)
accuracy	0	#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))
accuracy	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0	#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
accuracy	0	#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
accuracy	29.98788023102775	(PI.f32)
accuracy	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)

Samples

81.0ms

256×

invalid

Compiler

Compiled 791 to 49 computations (93.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 29.0ms (52.3% of total)

ival-div: 8.0ms (14.4% of total)

ival-add: 5.0ms (9% of total)

ival-pow: 4.0ms (7.2% of total)

ival-sub: 3.0ms (5.4% of total)

ival-log: 3.0ms (5.4% of total)

ival-pi: 2.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series76.0ms (0.7%)

Memory

7.1MiB live, 129.0MiB allocated

Counts

28 → 324

Calls

Call 1

Inputs
#s(alt (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())
#s(alt (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (patch (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) #<representation binary32>) () ())
#s(alt (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (patch (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #<representation binary32>) () ())
#s(alt (pow.f32 alpha #s(literal 4 binary32)) (patch (pow.f32 alpha #s(literal 4 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (patch #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) #<representation binary32>) () ())
#s(alt (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (patch (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) #<representation binary32>) () ())
#s(alt #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (patch #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (patch (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) #<representation binary32>) () ())
#s(alt (/.f32 alpha #s(literal 1 binary32)) (patch (/.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (patch (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) #<representation binary32>) () ())
#s(alt (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (patch (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (patch (fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) #<representation binary32>) () ())
#s(alt (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (patch (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #<representation binary32>) () ())
#s(alt (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))) (patch (fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (patch (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (patch (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (patch (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (PI.f32) (patch (PI.f32) #<representation binary32>) () ())
#s(alt (log.f32 (.f32 alpha alpha)) (patch (log.f32 (.f32 alpha alpha)) #<representation binary32>) () ())
#s(alt (.f32 alpha alpha) (patch (.f32 alpha alpha) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (patch (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #<representation binary32>) () ())
#s(alt #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (patch #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) #<representation binary32>) () ())
#s(alt #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (patch #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta)) #<representation binary32>) () ())
#s(alt (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (patch (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)) (patch #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)) #<representation binary32>) () ())

Outputs
#s(alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (taylor 0 alpha) (#s(alt (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) (patch (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))) #<representation binary32>) () ())) ())
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Calls

6 calls:

Time	Variable		Point	Expression
21.0ms	cosTheta	@	-inf	((/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (- 1 (pow alpha 4)) (pow alpha 4) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))
13.0ms	alpha	@	0	((/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (- 1 (pow alpha 4)) (pow alpha 4) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))
13.0ms	alpha	@	-inf	((/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (- 1 (pow alpha 4)) (pow alpha 4) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))
11.0ms	alpha	@	inf	((/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (- 1 (pow alpha 4)) (pow alpha 4) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))
3.0ms	cosTheta	@	inf	((/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (- 1 (pow alpha 4)) (pow alpha 4) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (+ (* alpha alpha) -1) (+ (* (/ alpha 1) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ -1 (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)))) (/ alpha (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (* alpha alpha)) (* (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) -1)) (/ (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (/ 0 0) (PI))) (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (PI) (log (* alpha alpha)) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (* cosTheta (+ (* alpha alpha) -1)) (* cosTheta (+ (* alpha alpha) -1)) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))

simplify144.0ms (1.4%)

Memory

-19.4MiB live, 214.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 034×	`lower-fma.f64`
6 034×	`lower-fma.f32`
5 420×	`lower-*.f64`
5 420×	`lower-*.f32`
3 150×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	351	5546
1	1147	5138
2	5390	4979
0	8159	4632

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 312

Calls

Call 1

Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* -1/2 (/ (* (pow cosTheta 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
1
(+ 1 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
alpha
alpha
alpha
alpha
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(/ 1 (+ 1 (* -1 (pow cosTheta 2))))
(+ (* -1 (/ (* (pow alpha 2) (pow cosTheta 2)) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (pow alpha 2) (- (/ (* (pow alpha 2) (pow cosTheta 4)) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (/ (* (pow alpha 2) (pow cosTheta 6)) (pow (+ 1 (* -1 (pow cosTheta 2))) 4))) (* -1 (/ (pow cosTheta 4) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (/ (pow cosTheta 2) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))) (/ 1 (+ 1 (* -1 (pow cosTheta 2)))))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha)))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
alpha
alpha
alpha
alpha
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(- (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha)))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))))) (* (pow alpha 6) (pow cosTheta 2)))) (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (pow alpha 6) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 4) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 4) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 4)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
alpha
alpha
alpha
alpha
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(/ 1 (* (pow alpha 2) (pow cosTheta 2)))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (/ 1 (pow cosTheta 2)))) (/ 1 (* (pow alpha 2) (pow cosTheta 4)))) (pow alpha 2))
(/ (- (+ (/ 1 (* (pow alpha 2) (pow cosTheta 2))) (+ (/ 1 (pow cosTheta 2)) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 6) (pow cosTheta 4))))) (+ (/ 1 (* (pow alpha 2) (pow cosTheta 4))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (pow cosTheta 2)) (/ 1 (pow cosTheta 4)))) (* (pow alpha 4) (pow cosTheta 2))))) (pow alpha 2))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))
(+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))
(+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* -1 (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 2))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))
(+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (* (pow cosTheta 2) (+ (* (pow cosTheta 2) (+ (* -1 (/ (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2)))))) (/ (* (pow cosTheta 2) (* (- 1 (pow alpha 4)) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))) (/ (* (- 1 (pow alpha 4)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (+ 1 (pow alpha 2))))))))
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
1
(+ 1 (* (pow cosTheta 2) (- 1 (pow alpha 2))))
(+ 1 (* (pow cosTheta 2) (- (+ 1 (* -1 (* (pow cosTheta 2) (* (- 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (pow alpha 2))))
(+ 1 (* (pow cosTheta 2) (- (+ 1 (* (pow cosTheta 2) (- (* (pow cosTheta 2) (* (- 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))) (* (- 1 (pow alpha 2)) (- (pow alpha 2) 1))))) (pow alpha 2))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(* -1 (/ (- 1 (pow alpha 4)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* -1 (/ (- 1 (pow alpha 4)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))

Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(fma.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
(- (* (pow alpha 2) (+ (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* (pow alpha 2) (+ (* -1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))) (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
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1
#s(literal 1 binary32)
(+ 1 (* -1 (pow alpha 4)))
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(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(pow alpha 4)
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(pow alpha 4)
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(pow alpha 4)
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(pow alpha 4)
(pow.f32 alpha #s(literal 4 binary32))
-1
#s(literal -1 binary32)
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(* (PI) (+ 1 (* -1 (pow cosTheta 2))))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(+ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (* (pow alpha 2) (* (pow cosTheta 2) (PI))))
(.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
alpha
alpha
alpha
alpha
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
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(- (pow alpha 2) 1)
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(fma.f32 alpha alpha #s(literal -1 binary32))
(/ 1 (+ 1 (* -1 (pow cosTheta 2))))
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(/.f32 (-.f32 (-.f32 (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))) (neg.f32 (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (PI.f32)) (.f32 (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 (-.f32 (/.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))) (.f32 cosTheta cosTheta))) (*.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- 1 (pow alpha 4)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (-.f32 (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))) (neg.f32 (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (PI.f32)) (.f32 (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 (-.f32 (/.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))) (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32)) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))))) (pow.f32 cosTheta #s(literal 6 binary32)))) (*.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(/ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta)
(/ (- (/ 1 (- (pow alpha 2) 1)) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)))) (pow cosTheta 2))
(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (pow cosTheta 4) (pow (- (pow alpha 2) 1) 3))) (/ 1 (- (pow alpha 2) 1))) (+ (/ 1 (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2))) (/ 1 (* (pow cosTheta 6) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32))) (pow.f32 cosTheta #s(literal 4 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 4 binary32))) (pow.f32 cosTheta #s(literal 6 binary32)))) (.f32 cosTheta cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(.f32 (.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (pow cosTheta 2))))
(.f32 (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta))) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))

rewrite24.0ms (0.2%)

Memory

13.6MiB live, 51.3MiB allocated

Rules

52×	`lower-*.f64`
50×	`lift-*.f32`
26×	`lift-/.f32`
26×	`lower-/.f64`
12×	`lift-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	447
0	131	447

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

28 → 33

Calls

Call 1

Inputs
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(pow.f32 alpha #s(literal 4 binary32))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))

Outputs
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(pow.f32 alpha #s(literal 4 binary32))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(+.f32 (.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha #s(literal 1 binary32))
(/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(+.f32 (.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(+.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32)))
(/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))
(+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.f32 alpha alpha)
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
#s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
#s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))

eval42.0ms (0.4%)

Memory: 14.8MiB live, 95.4MiB allocated
Compiler: Compiled 18 212 to 622 computations (96.6% saved)

prune229.0ms (2.2%)

Memory

-7.4MiB live, 349.2MiB allocated

Pruning

150 alts after pruning (137 fresh and 13 done)

	Pruned	Kept	Total
New	443	26	469
Fresh	7	111	118
Picked	0	5	5
Done	0	8	8
Total	450	150	600

Accuracy

99.6%

Counts

600 → 150

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32)))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
✓	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(approx ( alpha alpha) (*.f32 alpha alpha))))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
	-0.0%	(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
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	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 cosTheta cosTheta) alpha) alpha))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
✓	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 #s(approx (* alpha alpha) (*.f32 alpha alpha)) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	-0.0%	(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
	98.3%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.5%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	82.2%	(/.f32 (/.f32 #s(approx (- 1 (pow alpha 4)) #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))
✓	71.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	71.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 #s(approx (+ ( alpha cosTheta) cosTheta) (fma.f32 cosTheta alpha cosTheta)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.4%	(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	71.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
✓	-0.0%	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	7.9%	#s(approx (/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))) (PI.f32)))
	67.2%	#s(approx (/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))

Compiler

Compiled 11 419 to 3 511 computations (69.3% saved)

regimes226.0ms (2.2%)

Memory

-7.4MiB live, 340.6MiB allocated

Counts

175 → 1

Calls

Call 1

Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
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(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 #s(approx (+ ( alpha cosTheta) cosTheta) (fma.f32 cosTheta alpha cosTheta)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)) cosTheta))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) alpha)) (+.f32 (neg.f32 alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (- 1 (pow alpha 4)) #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta)))))
#s(approx (/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (log.f32 (.f32 alpha alpha)))) (PI.f32)))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 alpha #s(literal 4 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Calls

4 calls:

64.0ms	(*.f32 alpha alpha)
56.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
49.0ms	alpha
47.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.5%	1	`cosTheta`
98.5%	1	`alpha`
98.5%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes204.0ms (2%)

Memory

-1.1MiB live, 366.8MiB allocated

Counts

158 → 1

Calls

Call 1

Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
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(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32)))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))

Calls

4 calls:

61.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
49.0ms	cosTheta
44.0ms	(*.f32 alpha alpha)
42.0ms	alpha

Results

Accuracy	Segments	Branch
97.1%	1	`cosTheta`
97.1%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.1%	1	`alpha`
97.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes184.0ms (1.8%)

Memory

7.2MiB live, 322.5MiB allocated

Counts

155 → 1

Calls

Call 1

Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
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(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (log.f32 alpha)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (/ (- 1 (pow alpha 4)) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))

Calls

4 calls:

51.0ms	cosTheta
42.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
42.0ms	alpha
40.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
95.1%	1	`cosTheta`
95.1%	1	`alpha`
95.1%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
95.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes166.0ms (1.6%)

Memory

10.5MiB live, 259.5MiB allocated

Counts

149 → 1

Calls

Call 1

Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 #s(approx (/ 1 (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 #s(approx (/ 1 (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) #s(literal 1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) alpha) alpha)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
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(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) alpha))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(approx ( alpha alpha) (*.f32 alpha alpha))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32)))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))

Calls

4 calls:

41.0ms	(*.f32 alpha alpha)
40.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
39.0ms	cosTheta
38.0ms	alpha

Results

Accuracy	Segments	Branch
95.1%	1	`cosTheta`
95.1%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
95.1%	1	`alpha`
95.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes167.0ms (1.6%)

Memory

8.6MiB live, 323.8MiB allocated

Counts

148 → 1

Calls

Call 1

Inputs
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
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(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (.f32 alpha alpha) cosTheta)) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (.f32 alpha alpha))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(approx ( alpha alpha) (*.f32 alpha alpha))))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32)))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) #s(approx (+ ( (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (*.f32 alpha alpha)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))
(fma.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) (.f32 alpha alpha) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (PI.f32))) #s(literal -1 binary32)))

Outputs

(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (*.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (*.f32 (*.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (*.f32 (*.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))

Calls

4 calls:

41.0ms	alpha
40.0ms	(*.f32 alpha alpha)
40.0ms	cosTheta
38.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Results

Accuracy	Segments	Branch
3.4%	1	`cosTheta`
3.4%	1	`alpha`
3.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
3.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes28.0ms (0.3%)

Memory

-23.8MiB live, 15.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs

(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

Outputs

(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 #s(approx (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

Calls

4 calls:

22.0ms	(*.f32 alpha alpha)
2.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	alpha
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
-0.0%	1	`cosTheta`
-0.0%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
-0.0%	1	`alpha`
-0.0%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 29 to 20 computations (31% saved)

simplify68.0ms (0.7%)

Memory

-10.2MiB live, 70.1MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`-commutative-binary32-.f32`
12×	`+-commutative-binary32-+.f32`
10×	`sub-neg-binary32-neg.f32-+.f32--.f32`
6×	`neg-mul-1-binary32-*.f32-neg.f32`
6×	`neg-sub0-binary32--.f32-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	195
1	93	195
2	102	195
3	111	195
4	113	195

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (+.f32 (.f32 (.f32 cosTheta (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) cosTheta) #s(literal 1 binary32)) (.f32 (+.f32 (PI.f32) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ (* alpha cosTheta) cosTheta) (* (- alpha 1) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) cosTheta))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(fma.f32 alpha (/.f32 alpha (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 #s(approx (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1) (.f32 (.f32 cosTheta (*.f32 alpha alpha)) cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) #s(approx ( (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI.f32))))

soundness864.0ms (8.5%)

Memory

37.2MiB live, 871.2MiB allocated

Rules

8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
8 108×	`lower-*.f64`
8 108×	`lower-*.f32`
7 200×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	351	5546
1	1147	5138
2	5390	4979
0	8159	4632
0	630	6945
1	2131	6466
0	9040	6184
0	197	2350
1	582	2290
2	2231	2197
0	8702	2075
0	13	65
0	23	65
1	98	65
2	768	63
0	8446	55
0	332	4438
1	1008	4235
2	3836	4201
0	8526	3931

Stop Event

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

Compiler

Compiled 454 to 226 computations (50.2% saved)

preprocess46.0ms (0.4%)

Memory

-26.2MiB live, 135.3MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 832 to 448 computations (46.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze56.0ms (0.5%)

sample1.8s (17.6%)

explain205.0ms (2%)

preprocess202.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify193.0ms (1.9%)

localize36.0ms (0.4%)

series101.0ms (1%)

simplify193.0ms (1.9%)

rewrite406.0ms (4%)

eval464.0ms (4.5%)

prune378.0ms (3.7%)

simplify9.0ms (0.1%)

localize169.0ms (1.7%)

series254.0ms (2.5%)

simplify883.0ms (8.7%)

rewrite232.0ms (2.3%)

eval1.2s (12.2%)

prune163.0ms (1.6%)

simplify9.0ms (0.1%)

localize113.0ms (1.1%)

series67.0ms (0.7%)

simplify173.0ms (1.7%)

rewrite23.0ms (0.2%)

eval53.0ms (0.5%)

prune173.0ms (1.7%)

simplify10.0ms (0.1%)

localize137.0ms (1.3%)

series76.0ms (0.7%)

simplify144.0ms (1.4%)

rewrite24.0ms (0.2%)

eval42.0ms (0.4%)

prune229.0ms (2.2%)

regimes226.0ms (2.2%)

regimes204.0ms (2%)

regimes184.0ms (1.8%)

regimes166.0ms (1.6%)

regimes167.0ms (1.6%)

regimes28.0ms (0.3%)

simplify68.0ms (0.7%)

soundness864.0ms (8.5%)

preprocess46.0ms (0.4%)

end0.0ms (0%)

Profiling