Metrics for GTR1 distribution

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze79.0ms (1.1%)

Memory

5.0MiB live, 80.5MiB 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)

sample1.4s (20.5%)

Memory

61.1MiB live, 2 248.4MiB allocated

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 859.0ms

ival-mult: 326.0ms (38% of total)

const: 165.0ms (19.2% of total)

ival-log: 85.0ms (9.9% of total)

ival-<=: 81.0ms (9.4% of total)

ival-div: 62.0ms (7.2% of total)

ival-add: 39.0ms (4.5% of total)

ival-sub: 39.0ms (4.5% of total)

ival-pi: 28.0ms (3.3% of total)

ival-and: 22.0ms (2.6% of total)

exact: 10.0ms (1.2% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain170.0ms (2.4%)

Memory

-47.1MiB live, 344.5MiB 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

66.0ms

512×

valid

Compiler

Compiled 212 to 43 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 31.0ms (60.9% of total)

ival-log: 9.0ms (17.7% of total)

ival-div: 4.0ms (7.9% of total)

ival-pi: 2.0ms (3.9% of total)

ival-add: 2.0ms (3.9% of total)

ival-sub: 2.0ms (3.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess191.0ms (2.7%)

Memory

19.8MiB live, 292.0MiB 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 26 to 13 computations (50% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Status

Accuracy

Program

▶

98.6%

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

Compiler

Compiled 26 to 13 computations (50% saved)

simplify178.0ms (2.5%)

Memory

-11.8MiB live, 241.7MiB 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

localize32.0ms (0.5%)

Memory

-9.6MiB live, 66.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.13671875	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.203125	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.3046875	(/.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	0.3662300293053261	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

24.0ms

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 (41.8% of total)

ival-div: 3.0ms (17.9% of total)

ival-log: 3.0ms (17.9% of total)

ival-add: 2.0ms (11.9% of total)

ival-pi: 1.0ms (6% of total)

ival-sub: 1.0ms (6% of total)

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

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

exact: 0.0ms (0% of total)

series59.0ms (0.8%)

Memory

-2.3MiB live, 118.6MiB 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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#s(alt (* (pow cosTheta 2) (- (pow alpha 2) 1)) (taylor -inf cosTheta) (#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>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	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))
11.0ms	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))
8.0ms	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	@	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))

simplify170.0ms (2.4%)

Memory

15.0MiB live, 290.0MiB 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 #s(literal -1/2 binary32) (.f32 (.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 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (log.f32 alpha)))) alpha) alpha (/.f32 #s(literal -1/2 binary32) (.f32 (.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 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (log.f32 alpha)))) (.f32 (.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.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 #s(literal -1/2 binary32) (.f32 (.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 (/.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.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) (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (log.f32 alpha))))) (.f32 alpha alpha) (/.f32 #s(literal -1/2 binary32) (.f32 (.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 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (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))))))))
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(/.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.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 #s(literal 1 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)) (.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32)))))) (*.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)
(* (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 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (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 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.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 #s(literal 1 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.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 #s(literal 1 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)) (.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32)))))) (*.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)

rewrite207.0ms (2.9%)

Memory

-7.6MiB live, 347.7MiB 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) (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))
(*.f32 (+.f32 (neg.f32 alpha) #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) alpha))
(.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 (*.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 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 (fma.f32 (.f32 alpha alpha) (*.f32 alpha alpha) #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 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha))))
(.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (*.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (*.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))) (+.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (*.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (*.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (*.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))))))))
(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (*.f32 (neg.f32 alpha) alpha))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)))) (neg.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)))) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)))) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #s(literal -1 binary32)) (fma.f32 (.f32 alpha alpha) alpha #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 (fma.f32 (.f32 alpha alpha) alpha #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)) (fma.f32 (.f32 alpha alpha) alpha #s(literal 1 binary32))) (*.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #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)) (fma.f32 (.f32 alpha alpha) alpha #s(literal -1 binary32))) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (*.f32 alpha alpha) alpha) alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal 1 binary32)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha))) (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)))) (fma.f32 (.f32 (*.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha alpha #s(literal -1 binary32)))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32))) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32))) (neg.f32 (-.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha #s(literal 1 binary32)) (*.f32 (neg.f32 alpha) alpha))))
(/.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32))) (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (neg.f32 (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #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 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #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))))
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(.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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) cosTheta)) (fma.f32 (neg.f32 alpha) alpha #s(literal -1 binary32)))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) cosTheta) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (.f32 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))))

eval117.0ms (1.7%)

Memory: 21.4MiB live, 210.0MiB allocated
Compiler: Compiled 33 548 to 2 788 computations (91.7% saved)

prune213.0ms (3%)

Memory

8.0MiB live, 415.0MiB allocated

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	853	30	883
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	854	30	884

Accuracy

99.7%

Counts

884 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
	98.2%	(/.f32 (fma.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))))
▶	-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))))
	98.2%	(/.f32 (/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha (fma.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))))
	98.2%	(/.f32 (/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #s(literal -1 binary32)) (-.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha #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))))
	97.5%	(/.f32 (/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #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 (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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.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))))
	97.9%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.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))))
▶	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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)) (fma.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))))
	97.7%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #s(literal -1 binary32)) (fma.f32 (.f32 alpha alpha) alpha #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) alpha #s(literal 1 binary32)) (.f32 (neg.f32 alpha) alpha)) (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.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))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.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))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.6%	(/.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))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	98.6%	(/.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 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32))))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta)))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))))))
	96.6%	(/.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)))))
	93.1%	(/.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))))
▶	98.1%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.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))))
	98.1%	(/.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))))
	65.3%	(/.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))))
	97.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (log.f32 alpha)))) alpha) alpha (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha)))))
	93.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	65.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
	95.7%	#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)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (/.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))

Compiler

Compiled 2 236 to 1 038 computations (53.6% saved)

simplify11.0ms (0.2%)

Memory

-17.8MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

42×	`lower-*.f64`
38×	`lift-*.f32`
16×	`lift-/.f32`
16×	`lower-+.f64`
16×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	605
0	89	605

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

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

localize123.0ms (1.8%)

Memory

20.2MiB live, 297.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
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)
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)
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)
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 (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

85.0ms

256×

invalid

Compiler

Compiled 639 to 50 computations (92.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 31.0ms (51.7% of total)

ival-div: 10.0ms (16.7% of total)

ival-add: 8.0ms (13.3% of total)

ival-log: 5.0ms (8.3% of total)

ival-sub: 3.0ms (5% of total)

ival-pi: 2.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series161.0ms (2.3%)

Memory

-1.8MiB live, 356.3MiB allocated

Counts

23 → 336

Calls

Call 1

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

Outputs
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Calls

6 calls:

Time	Variable		Point	Expression
49.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (* cosTheta (+ (* alpha alpha) -1)) (log alpha) (* (log alpha) (+ (PI) (PI))))
29.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (* cosTheta (+ (* alpha alpha) -1)) (log alpha) (* (log alpha) (+ (PI) (PI))))
25.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (* cosTheta (+ (* alpha alpha) -1)) (log alpha) (* (log alpha) (+ (PI) (PI))))
18.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (* cosTheta (+ (* alpha alpha) -1)) (log alpha) (* (log alpha) (+ (PI) (PI))))
13.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* (PI) (log (* alpha alpha))) (* cosTheta (+ (* alpha alpha) -1)) (log alpha) (* (log alpha) (+ (PI) (PI))))

simplify196.0ms (2.8%)

Memory

15.0MiB live, 365.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 860×	`lower-fma.f64`
7 860×	`lower-fma.f32`
7 404×	`lower-*.f64`
7 404×	`lower-*.f32`
4 774×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	795	12233
1	2727	11546
0	9013	10925

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

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

rewrite44.0ms (0.6%)

Memory

-14.2MiB live, 79.6MiB allocated

Rules

42×	`lower-*.f64`
38×	`lift-*.f32`
16×	`lift-/.f32`
16×	`lower-/.f64`
16×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	330
0	89	330

Stop Event

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

Counts

23 → 25

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

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

eval54.0ms (0.8%)

Memory: -3.0MiB live, 152.2MiB allocated
Compiler: Compiled 26 487 to 848 computations (96.8% saved)

prune143.0ms (2%)

Memory

-17.1MiB live, 185.9MiB allocated

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	592	22	614
Fresh	11	14	25
Picked	5	0	5
Done	0	0	0
Total	608	36	644

Accuracy

99.8%

Counts

644 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
	98.2%	(/.f32 (fma.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))))
▶	-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))))
	97.5%	(/.f32 (/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #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 (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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.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))))
	97.9%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.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))))
▶	96.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #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 (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 #s(approx (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 6 binary32)))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.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))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.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))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.5%	(/.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 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	98.6%	(/.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 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32))))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))))))
	96.6%	(/.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)))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (.f32 cosTheta cosTheta) (/.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
	54.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha) (/.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))))) (*.f32 cosTheta cosTheta))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	93.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	96.1%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #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))))
	80.6%	(/.f32 (.f32 #s(approx (+ ( (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.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))))
	98.0%	(/.f32 #s(approx (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) 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 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta)))))
▶	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 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))))
▶	65.3%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	92.4%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (-.f32 (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)))))
	65.3%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32)))))
	93.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
	1.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
	93.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.0%	#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha)))))
	92.6%	#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))

Compiler

Compiled 2 392 to 1 182 computations (50.6% saved)

simplify9.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

40×	`lower-*.f64`
36×	`lift-*.f32`
16×	`lift-/.f32`
16×	`lower-/.f64`
12×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	605
0	94	605

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

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

localize182.0ms (2.6%)

Memory

2.7MiB live, 199.7MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

136.0ms

256×

invalid

Compiler

Compiled 591 to 43 computations (92.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-mult: 89.0ms (79.1% of total)

ival-div: 9.0ms (8% of total)

ival-add: 5.0ms (4.4% of total)

ival-log: 5.0ms (4.4% of total)

ival-sub: 3.0ms (2.7% of total)

ival-pi: 1.0ms (0.9% of total)

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

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

exact: 0.0ms (0% of total)

series169.0ms (2.4%)

Memory

10.3MiB live, 214.9MiB allocated

Counts

25 → 348

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
38.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (+ (* 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (log alpha) (+ (PI) (PI))) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha alpha) -1)) (/ 0 0) (log alpha))
37.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (+ (* 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (log alpha) (+ (PI) (PI))) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha alpha) -1)) (/ 0 0) (log alpha))
35.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (+ (* 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (log alpha) (+ (PI) (PI))) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha alpha) -1)) (/ 0 0) (log alpha))
18.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (+ (* 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (log alpha) (+ (PI) (PI))) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha alpha) -1)) (/ 0 0) (log alpha))
6.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (+ (* 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 alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (log alpha) (+ (PI) (PI))) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha alpha) -1)) (/ 0 0) (log alpha))

simplify201.0ms (2.9%)

Memory

1.9MiB live, 356.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 708×	`lower-*.f64`
7 708×	`lower-*.f32`
7 444×	`lower-fma.f64`
7 444×	`lower-fma.f32`
3 992×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	621	10624
1	2112	10255
0	8797	9727

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 346

Calls

Call 1

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

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

rewrite22.0ms (0.3%)

Memory

6.9MiB live, 45.9MiB allocated

Rules

40×	`lower-*.f64`
36×	`lift-*.f32`
16×	`lift-/.f32`
16×	`lower-/.f64`
12×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	352
0	94	352

Stop Event

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

Counts

25 → 26

Calls

Call 1

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

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

eval186.0ms (2.6%)

Memory: -6.0MiB live, 114.6MiB allocated
Compiler: Compiled 22 158 to 700 computations (96.8% saved)

prune92.0ms (1.3%)

Memory

-12.8MiB live, 146.2MiB allocated

Pruning

39 alts after pruning (39 fresh and 0 done)

	Pruned	Kept	Total
New	554	19	573
Fresh	11	20	31
Picked	5	0	5
Done	0	0	0
Total	570	39	609

Accuracy

99.9%

Counts

609 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
	98.2%	(/.f32 (fma.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))))
	97.5%	(/.f32 (/.f32 (fma.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 alpha alpha) alpha) #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 (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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.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))))
▶	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #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 (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%	(/.f32 (/.f32 #s(approx (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 6 binary32)))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.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))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
▶	98.6%	(/.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 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32))))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (.f32 cosTheta cosTheta) (/.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
	54.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha) (/.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))))) (*.f32 cosTheta cosTheta))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
	93.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	96.1%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #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))))
	80.6%	(/.f32 (.f32 #s(approx (+ ( (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.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))))
	96.0%	(/.f32 #s(approx (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	98.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta)))))
	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
	92.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	54.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha) (/.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))))) (*.f32 cosTheta cosTheta))))
	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 alpha)) (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))))
▶	98.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) 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))))
	65.3%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
	65.3%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
	63.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
▶	-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))))
	92.4%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (-.f32 (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)))))
	92.4%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (log.f32 (.f32 alpha alpha)))))
	65.3%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32)))))
	93.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
	93.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.0%	#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha)))))
	92.6%	#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))

Compiler

Compiled 2 346 to 1 236 computations (47.3% saved)

simplify10.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

44×	`lower-*.f64`
32×	`lift-*.f32`
22×	`lower-/.f64`
20×	`lift-/.f32`
20×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	721
0	111	718

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

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

localize174.0ms (2.5%)

Memory

-26.6MiB live, 210.1MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

109.0ms

256×

invalid

Compiler

Compiled 703 to 55 computations (92.2% saved)

Precisions

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

ival-mult: 50.0ms (56.9% of total)

ival-div: 19.0ms (21.6% of total)

ival-add: 9.0ms (10.2% of total)

ival-log: 5.0ms (5.7% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series232.0ms (3.3%)

Memory

7.9MiB live, 252.2MiB allocated

Counts

25 → 360

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
55.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (/ (+ (* 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 alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (+ (* (* alpha alpha) alpha) -1) (PI) (log (* alpha alpha)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta) (log alpha) (* (PI) (log (* alpha alpha))))
49.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (/ (+ (* 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 alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (+ (* (* alpha alpha) alpha) -1) (PI) (log (* alpha alpha)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta) (log alpha) (* (PI) (log (* alpha alpha))))
49.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (/ (+ (* 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 alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (+ (* (* alpha alpha) alpha) -1) (PI) (log (* alpha alpha)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta) (log alpha) (* (PI) (log (* alpha alpha))))
47.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (/ (+ (* 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 alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (+ (* (* alpha alpha) alpha) -1) (PI) (log (* alpha alpha)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta) (log alpha) (* (PI) (log (* alpha alpha))))
6.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (/ (+ (* 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 alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (+ (* (* alpha alpha) alpha) -1) (PI) (log (* alpha alpha)) (* cosTheta cosTheta) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta) (log alpha) (* (PI) (log (* alpha alpha))))

simplify271.0ms (3.9%)

Memory

28.8MiB live, 306.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 698×	`lower-fma.f64`
8 698×	`lower-fma.f32`
8 138×	`lower-*.f64`
8 138×	`lower-*.f32`
3 296×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	710	10881
1	2325	10545
0	8174	10051

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 358

Calls

Call 1

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

rewrite70.0ms (1%)

Memory

-32.9MiB live, 43.6MiB allocated

Rules

44×	`lower-*.f64`
32×	`lift-*.f32`
22×	`lower-/.f64`
20×	`lift-/.f32`
20×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	403
0	111	400

Stop Event

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

Counts

25 → 26

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

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

eval76.0ms (1.1%)

Memory: 19.0MiB live, 97.4MiB allocated
Compiler: Compiled 23 309 to 776 computations (96.7% saved)

prune126.0ms (1.8%)

Memory

-9.5MiB live, 194.7MiB allocated

Pruning

41 alts after pruning (40 fresh and 1 done)

	Pruned	Kept	Total
New	560	11	571
Fresh	5	29	34
Picked	4	1	5
Done	0	0	0
Total	569	41	610

Accuracy

99.9%

Counts

610 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
	98.2%	(/.f32 (fma.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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.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))))
	97.6%	(/.f32 (/.f32 (.f32 #s(approx (+ ( (* alpha alpha) alpha) -1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) alpha))) alpha) (.f32 alpha alpha))) (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 (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%	(/.f32 (/.f32 #s(approx (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 6 binary32)))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	81.9%	(/.f32 (/.f32 #s(approx (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (fma.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.2%	(/.f32 (/.f32 #s(approx (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (.f32 (neg.f32 (pow.f32 alpha #s(literal 5 binary32))) (+.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) alpha)) (-.f32 (/.f32 #s(literal 1 binary32) (.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 (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 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.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))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32))))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (.f32 cosTheta cosTheta) (/.f32 (.f32 (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
	54.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha) (/.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))))) (*.f32 cosTheta cosTheta))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	93.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
	96.1%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #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))))
	80.6%	(/.f32 (.f32 #s(approx (+ ( (* alpha alpha) (* alpha alpha)) -1) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.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%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	96.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	98.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.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 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal -1 binary32))))))
	98.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta)))))
	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
	96.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	92.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	54.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha) (/.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))))) (*.f32 cosTheta cosTheta))))
	97.9%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 alpha)) (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))))
	96.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	65.3%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
	65.3%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	65.3%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
	63.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
✓	-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))))
	92.4%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (-.f32 (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)))))
	92.4%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (log.f32 (.f32 alpha alpha)))))
	65.3%	#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
	92.5%	#s(approx (/ (/ (* (+ (* (* alpha alpha) alpha) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ 1 alpha)) (- alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32)))))
	95.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1/2 binary32)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32)))))
	93.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
	93.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.0%	#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha)))))
	92.6%	#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))

Compiler

Compiled 3 653 to 948 computations (74% saved)

regimes136.0ms (1.9%)

Memory

1.6MiB live, 160.2MiB allocated

Counts

83 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) 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))))
#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #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)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
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(/.f32 (/.f32 #s(approx (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (.f32 (.f32 alpha alpha) alpha) alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 6 binary32)))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.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))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) #s(literal 1/2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (log.f32 alpha)))) alpha) alpha (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha)))))
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (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 (.f32 (.f32 (.f32 alpha alpha) alpha) alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.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 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.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 #s(literal 1 binary32) alpha) (*.f32 (*.f32 (-.f32 alpha #s(literal 1 binary32)) cosTheta) cosTheta)))))

Calls

4 calls:

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))))
35.0ms	cosTheta
29.0ms	alpha
26.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`alpha`
98.6%	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))))`
98.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes66.0ms (0.9%)

Memory

-6.0MiB live, 73.1MiB allocated

Counts

36 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) 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))))
#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #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)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (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 (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 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) 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))))

Outputs

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

Calls

4 calls:

30.0ms	cosTheta
13.0ms	(/.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))))
10.0ms	alpha
10.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`alpha`
98.6%	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))))`
98.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes41.0ms (0.6%)

Memory

4.0MiB live, 43.3MiB allocated

Counts

31 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) 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))))
#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))

Outputs

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

Calls

4 calls:

9.0ms	(/.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))))
9.0ms	(*.f32 alpha alpha)
9.0ms	cosTheta
9.0ms	alpha

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 37 to 20 computations (45.9% saved)

regimes52.0ms (0.7%)

Memory

5.4MiB live, 41.3MiB allocated

Counts

29 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (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 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) 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))))
#s(approx (/ (* (+ (* (* alpha alpha) (* alpha alpha)) -1) (/ 1 (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))))

Outputs

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

Calls

4 calls:

26.0ms	alpha
8.0ms	(*.f32 alpha alpha)
8.0ms	(/.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))))
8.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.6%	1	`cosTheta`
96.6%	1	`alpha`
96.6%	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))))`
96.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes50.0ms (0.7%)

Memory

-4.0MiB live, 32.1MiB allocated

Counts

23 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (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)))))

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:

28.0ms	cosTheta
7.0ms	(/.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))))
7.0ms	alpha
7.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
96.6%	1	`cosTheta`
96.6%	1	`alpha`
96.6%	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))))`
96.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes27.0ms (0.4%)

Memory

30.1MiB live, 30.1MiB allocated

Counts

22 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #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 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))

Outputs

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

Calls

4 calls:

7.0ms	(/.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))))
7.0ms	(*.f32 alpha alpha)
7.0ms	alpha
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.5%	1	`cosTheta`
96.5%	1	`alpha`
96.5%	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))))`
96.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes45.0ms (0.6%)

Memory

-6.9MiB live, 29.2MiB allocated

Counts

20 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

25.0ms	(*.f32 alpha alpha)
6.0ms	(/.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))))
6.0ms	alpha
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.5%	1	`cosTheta`
96.5%	1	`alpha`
96.5%	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))))`
96.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes32.0ms (0.5%)

Memory

-18.7MiB live, 28.1MiB allocated

Counts

19 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
#s(approx (/ (/ (- (* (* (* (* alpha alpha) alpha) alpha) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1)))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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))))

Outputs

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

Calls

4 calls:

13.0ms	alpha
6.0ms	(/.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))))
6.0ms	cosTheta
6.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
93.1%	1	`cosTheta`
93.1%	1	`alpha`
93.1%	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))))`
93.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes14.0ms (0.2%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

9 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (+ 1 alpha) (* (* (- alpha 1) cosTheta) cosTheta))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ (+ (* (* cosTheta cosTheta) (+ (* alpha alpha) -1)) -1) (+ (* (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta)) -1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

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

Calls

4 calls:

3.0ms	(/.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))))
3.0ms	(*.f32 alpha alpha)
3.0ms	cosTheta
3.0ms	alpha

Results

Accuracy	Segments	Branch
93.0%	1	`cosTheta`
93.0%	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))))`
93.0%	1	`alpha`
93.0%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes19.0ms (0.3%)

Memory

-22.7MiB live, 14.0MiB allocated

Counts

5 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))

Outputs

(/.f32 #s(approx (- (* alpha alpha) 1) #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:

11.0ms	cosTheta
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	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
63.6%	1	`cosTheta`
63.6%	1	`alpha`
63.6%	1	`(*.f32 alpha alpha)`
63.6%	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))))`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes8.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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:

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	cosTheta
2.0ms	alpha
2.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
-0.0%	1	`alpha`
-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	`(*.f32 alpha alpha)`
-0.0%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify8.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Rules

34×	`*-commutative_binary32`
18×	`+-commutative_binary32`
12×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	330
1	108	330
2	118	330
3	128	330
4	129	330

Stop Event

1×

saturated

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

soundness1.0s (14.4%)

Memory

7.6MiB live, 718.5MiB allocated

Rules

8 698×	`lower-fma.f64`
8 698×	`lower-fma.f32`
8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
8 138×	`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
0	710	10881
1	2325	10545
0	8174	10051
0	197	2350
1	582	2290
2	2231	2197
0	8702	2075
0	621	10624
1	2112	10255
0	8797	9727
0	795	12233
1	2727	11546
0	9013	10925

Stop Event

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

Compiler

Compiled 1 064 to 388 computations (63.5% saved)

preprocess108.0ms (1.5%)

Memory

8.3MiB live, 167.3MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 1 552 to 764 computations (50.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze79.0ms (1.1%)

sample1.4s (20.5%)

explain170.0ms (2.4%)

preprocess191.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify178.0ms (2.5%)

localize32.0ms (0.5%)

series59.0ms (0.8%)

simplify170.0ms (2.4%)

rewrite207.0ms (2.9%)

eval117.0ms (1.7%)

prune213.0ms (3%)

simplify11.0ms (0.2%)

localize123.0ms (1.8%)

series161.0ms (2.3%)

simplify196.0ms (2.8%)

rewrite44.0ms (0.6%)

eval54.0ms (0.8%)

prune143.0ms (2%)

simplify9.0ms (0.1%)

localize182.0ms (2.6%)

series169.0ms (2.4%)

simplify201.0ms (2.9%)

rewrite22.0ms (0.3%)

eval186.0ms (2.6%)

prune92.0ms (1.3%)

simplify10.0ms (0.1%)

localize174.0ms (2.5%)

series232.0ms (3.3%)

simplify271.0ms (3.9%)

rewrite70.0ms (1%)

eval76.0ms (1.1%)

prune126.0ms (1.8%)

regimes136.0ms (1.9%)

regimes66.0ms (0.9%)

regimes41.0ms (0.6%)

regimes52.0ms (0.7%)

regimes50.0ms (0.7%)

regimes27.0ms (0.4%)

regimes45.0ms (0.6%)

regimes32.0ms (0.5%)

regimes14.0ms (0.2%)

regimes19.0ms (0.3%)

regimes8.0ms (0.1%)

simplify8.0ms (0.1%)

soundness1.0s (14.4%)

preprocess108.0ms (1.5%)

end0.0ms (0%)

Profiling