Metrics for GTR1 distribution

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze85.0ms (0.7%)

Memory

-18.9MiB live, 69.7MiB 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)

sample2.1s (17.3%)

Memory

-23.9MiB live, 2 258.4MiB allocated

Samples

1.8s

8 256×

valid

Precisions

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

ival-mult: 892.0ms (61.5% of total)

ival-log: 150.0ms (10.3% of total)

const: 112.0ms (7.7% of total)

ival-<=: 80.0ms (5.5% of total)

ival-div: 60.0ms (4.1% of total)

ival-add: 47.0ms (3.2% of total)

ival-sub: 39.0ms (2.7% of total)

ival-pi: 33.0ms (2.3% of total)

ival-and: 23.0ms (1.6% of total)

exact: 11.0ms (0.8% of total)

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

Bogosity

explain165.0ms (1.4%)

Memory

41.0MiB live, 315.8MiB 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	2	254

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0.0

Recall?

0/0

Samples

57.0ms

512×

valid

Compiler

Compiled 212 to 43 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 15.0ms (43.1% of total)

ival-log: 9.0ms (25.8% of total)

ival-div: 4.0ms (11.5% of total)

ival-pi: 2.0ms (5.7% of total)

ival-add: 2.0ms (5.7% of total)

ival-sub: 2.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess314.0ms (2.6%)

Memory

-45.2MiB live, 401.5MiB 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 (PI.f32) (*.f32 (log.f32 (*.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))))

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

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(/.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

▶

98.4%

(/.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)

simplify255.0ms (2.1%)

Memory

24.2MiB live, 340.7MiB 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 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))
(-.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 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta 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 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #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 cosTheta cosTheta))
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
cosTheta

localize45.0ms (0.4%)

Memory

-14.6MiB live, 48.7MiB 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	0.1875	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.28515625	(/.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	0.40625	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

33.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sub: 11.0ms (43.5% of total)

ival-mult: 7.0ms (27.7% of total)

ival-log: 3.0ms (11.9% of total)

ival-div: 2.0ms (7.9% of total)

ival-pi: 1.0ms (4% of total)

ival-add: 1.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series54.0ms (0.4%)

Memory

4.8MiB live, 92.7MiB 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 (pow alpha 2) (taylor inf 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 (/ 1 (pow alpha 2)))) (taylor inf 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 (/ 1 (pow alpha 2)))) (taylor inf 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 (/ 1 (pow alpha 2)))) (taylor inf 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 -inf 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 (/ 1 (pow alpha 2)))) (taylor -inf 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 (/ 1 (pow alpha 2)))) (taylor -inf 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 (/ 1 (pow alpha 2)))) (taylor -inf 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 (* (pow alpha 2) (pow cosTheta 2)) (taylor inf 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 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2)))) (taylor inf 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 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2)))) (taylor inf 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 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2)))) (taylor inf 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 (* (pow alpha 2) (pow cosTheta 2)) (taylor -inf 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 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2)))) (taylor -inf 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 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2)))) (taylor -inf 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 (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2)))) (taylor -inf 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 (taylor 0 cosTheta) (#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 (* (pow cosTheta 2) (- (pow alpha 2) 1))) (taylor 0 cosTheta) (#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 (* (pow cosTheta 2) (- (pow alpha 2) 1))) (taylor 0 cosTheta) (#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>) () ())) ())
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Calls

33 calls:

Time	Variable		Point	Expression
29.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
9.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify317.0ms (2.6%)

Memory

11.9MiB live, 486.4MiB 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	8730	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)
(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) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
1
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(+ 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))
(* (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))
(/ -1/2 (* (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))))))))
(/ -1/2 (* (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))))))
(/ -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) 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)))))
(/ 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))
(/ 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 alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 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)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* -1 (pow cosTheta 2))
(+ (* -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 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 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 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) (- (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) (- (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))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(fma.f32 alpha alpha #s(literal -1 binary32))
(+ 1 (* -1 (pow cosTheta 2)))
(-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 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 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 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 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(fma.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 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 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 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 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))))) #s(literal 1 binary32))
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (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 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.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 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (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))))))))
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(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -1 cosTheta)
(neg.f32 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* cosTheta (- (pow alpha 2) 1))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(* 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 (pow cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (.f32 alpha alpha))))))
(* (pow alpha 2) (pow cosTheta 2))
(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (.f32 alpha alpha))))))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))
(.f32 alpha (.f32 alpha (.f32 cosTheta (-.f32 cosTheta (/.f32 cosTheta (.f32 alpha alpha))))))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))

rewrite307.0ms (2.5%)

Memory

-54.6MiB live, 430.8MiB 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
(neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(+.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(+.f32 (/.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(+.f32 (neg.f32 (neg.f32 (*.f32 alpha alpha))) #s(literal -1 binary32))
(+.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(+.f32 (*.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
(+.f32 (.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))))
(+.f32 (.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))) (.f32 alpha (+.f32 alpha #s(literal -1 binary32))))
(pow.f32 (/.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))
(fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
(fma.f32 alpha (+.f32 alpha #s(literal -1 binary32)) (*.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32))))
(fma.f32 (*.f32 alpha alpha) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 alpha alpha) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal -1 binary32)) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32))))
(fma.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(fma.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (+.f32 alpha #s(literal 1 binary32)) alpha (*.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32)))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 alpha #s(literal -1 binary32)) alpha))
(fma.f32 (exp.f32 (log.f32 alpha)) (exp.f32 (log.f32 alpha)) #s(literal -1 binary32))
(fma.f32 (/.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 alpha #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(fma.f32 (*.f32 #s(literal 1 binary32) alpha) alpha #s(literal -1 binary32))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(-.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(-.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(-.f32 (/.f32 (.f32 (.f32 alpha alpha) (*.f32 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 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (.f32 alpha alpha))) (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) #s(literal -1 binary32))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha))))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 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 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (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 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (neg.f32 (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 (-.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal 1 binary32)) (neg.f32 (*.f32 alpha alpha)))))
(/.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)))
(/.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 (.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(literal 1 binary32))) (.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 alpha alpha) (.f32 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 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal 1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (*.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) #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 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32))) (*.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha)))
(/.f32 (.f32 (fma.f32 alpha (.f32 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 alpha (.f32 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 alpha (.f32 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 alpha #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (.f32 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 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.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)))
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(fma.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 cosTheta #s(literal -1 binary32))))
(fma.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)))
(fma.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta (.f32 (.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta (*.f32 (neg.f32 cosTheta) cosTheta))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
(/.f32 (*.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal 1 binary32)))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 #s(literal 1 binary32) (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta))
(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta)
(.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) #s(literal 1 binary32))
(.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (fma.f32 alpha cosTheta cosTheta) (.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (.f32 (*.f32 cosTheta cosTheta) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal 1 binary32))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) cosTheta))
(.f32 (.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (+.f32 alpha #s(literal -1 binary32)))
(.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (*.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))))
(.f32 (.f32 (.f32 cosTheta cosTheta) (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 (*.f32 cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32))) (+.f32 alpha #s(literal 1 binary32)))

eval77.0ms (0.6%)

Memory: 20.8MiB live, 161.4MiB allocated
Compiler: Compiled 33 548 to 2 790 computations (91.7% saved)

prune173.0ms (1.4%)

Memory

13.2MiB live, 344.8MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	856	27	883
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	857	27	884

Accuracy

99.9%

Counts

884 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
	98.4%	(/.f32 (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))))
	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 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))))
	98.0%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 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))))
	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))))
	98.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (neg.f32 (.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))))
▶	97.8%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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))))
	97.8%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (.f32 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))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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 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))))
	98.1%	(/.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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) #s(literal 1 binary32))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	97.4%	(/.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)))))
	94.8%	(/.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 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (.f32 (+.f32 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))))
	66.9%	(/.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))))
	97.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.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 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))))
	98.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 alpha (.f32 alpha (fma.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.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 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (neg.f32 (/.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.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 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))
	94.8%	#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 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	66.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1 904 to 912 computations (52.1% saved)

simplify12.0ms (0.1%)

Memory

-35.1MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	553
0	83	551

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

localize154.0ms (1.3%)

Memory

15.3MiB live, 257.1MiB 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	29.987880231027383	(PI.f32)
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(neg.f32 (+.f32 alpha #s(literal 1 binary32)))
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	29.987880231027383	(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	29.987880231027383	(PI.f32)
accuracy	0	(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
accuracy	0	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))
accuracy	0	(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
accuracy	29.987880231027383	(PI.f32)
accuracy	0	(*.f32 cosTheta cosTheta)
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	29.987880231027383	(PI.f32)

Samples

86.0ms

256×

invalid

Compiler

Compiled 596 to 48 computations (91.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 30.0ms (51.6% of total)

ival-div: 12.0ms (20.7% of total)

ival-add: 9.0ms (15.5% of total)

ival-log: 3.0ms (5.2% of total)

ival-sub: 2.0ms (3.4% of total)

ival-pi: 1.0ms (1.7% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series48.0ms (0.4%)

Memory

3.8MiB live, 93.7MiB 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))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.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))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta 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 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))) #<representation binary32>) () ())
#s(alt (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))) (patch (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))) #<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 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))) (patch (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))) #<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 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) 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 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))) (patch (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (patch (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) #<representation binary32>) () ())
#s(alt (/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.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 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.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 alpha (+.f32 alpha #s(literal 1 binary32))) (patch (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (+.f32 alpha #s(literal 1 binary32)) (patch (+.f32 alpha #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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 alpha (.f32 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 alpha (.f32 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 alpha (.f32 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 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (patch (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (patch (fma.f32 alpha (.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 cosTheta) (patch (.f32 cosTheta cosTheta) #<representation binary32>) () ())
#s(alt (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (patch (.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) #<representation binary32>) () ())
#s(alt (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) (patch (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) #<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 (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<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))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.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))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta 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))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.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))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))))) #<representation binary32>) () ())) ())
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#s(alt (- (* -1 alpha) 1) (taylor 0 alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (- (* -1 alpha) 1) (taylor 0 alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (- (* -1 alpha) 1) (taylor 0 alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 alpha) (taylor inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* alpha (+ 1 (/ 1 alpha)))) (taylor inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* alpha (+ 1 (/ 1 alpha)))) (taylor inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* alpha (+ 1 (/ 1 alpha)))) (taylor inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 alpha) (taylor -inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* alpha (+ 1 (/ 1 alpha)))) (taylor -inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* alpha (+ 1 (/ 1 alpha)))) (taylor -inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* alpha (+ 1 (/ 1 alpha)))) (taylor -inf alpha) (#s(alt (neg.f32 (+.f32 alpha #s(literal 1 binary32))) (patch (neg.f32 (+.f32 alpha #s(literal 1 binary32))) #<representation binary32>) () ())) ())

Calls

99 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))))
2.0ms	alpha	@	0	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify255.0ms (2.1%)

Memory

12.2MiB live, 387.9MiB allocated

Algorithm

1×	egg-herbie

Rules

5 858×	`lower-*.f64`
5 858×	`lower-*.f32`
5 352×	`lower-fma.f64`
5 352×	`lower-fma.f32`
3 370×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	468	10368
1	1562	9952
2	7068	9888
0	8086	9428

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 345

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

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

rewrite77.0ms (0.6%)

Memory

-19.7MiB live, 35.3MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	293
0	83	291

Stop Event

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

Counts

25 → 28

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

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

eval378.0ms (3.1%)

Memory: 6.7MiB live, 93.0MiB allocated
Compiler: Compiled 26 030 to 645 computations (97.5% saved)

prune90.0ms (0.7%)

Memory

9.7MiB live, 123.9MiB allocated

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	682	20	702
Fresh	12	10	22
Picked	5	0	5
Done	0	0	0
Total	699	30	729

Accuracy

99.9%

Counts

729 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 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))))
	98.3%	(/.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))))
	98.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.8%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.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))))
	97.8%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (.f32 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))))
▶	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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 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))))
	84.6%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) 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 (+.f32 #s(literal -1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha))))) (neg.f32 (pow.f32 alpha #s(literal 5 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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) #s(literal 1 binary32))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	97.4%	(/.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 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))
	97.2%	(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 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))))
	98.3%	(/.f32 (.f32 (+.f32 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))))
	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 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	66.9%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	94.2%	#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 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	66.8%	#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 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	97.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))))) (fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (*.f32 (PI.f32) (log.f32 alpha))))))
	94.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	94.8%	#s(approx (/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (-.f32 (fma.f32 alpha alpha alpha) alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))

Compiler

Compiled 1 896 to 1 010 computations (46.7% saved)

simplify21.0ms (0.2%)

Memory

-25.4MiB live, 21.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f32 alpha (*.f32 alpha alpha) #s(literal -1 binary32))
cost-diff	0	(.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 (.f32 (fma.f32 alpha (.f32 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 alpha #s(literal -1 binary32))))
cost-diff	0	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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 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	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)))
cost-diff	0	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
cost-diff	0	#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 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
cost-diff	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 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 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
cost-diff	0	(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
cost-diff	0	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32)))
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 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 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)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))

Rules

60×	`lower-*.f64`
42×	`lift-*.f32`
28×	`lower-+.f64`
22×	`lower-/.f64`
20×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	736
0	140	734

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

localize473.0ms (3.9%)

Memory

38.4MiB live, 223.8MiB 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	29.987880231027383	(PI.f32)
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	0	#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 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
accuracy	29.987880231027383	(PI.f32)
accuracy	0	(*.f32 alpha alpha)
accuracy	0	(log.f32 (*.f32 alpha alpha))
accuracy	0	#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
accuracy	29.987880231027383	(PI.f32)
accuracy	0	(.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)))
accuracy	0	(neg.f32 cosTheta)
accuracy	0	#s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))
accuracy	29.987880231027383	(PI.f32)
accuracy	0	(neg.f32 cosTheta)
accuracy	0	(log.f32 alpha)
accuracy	0	#s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
accuracy	29.987880231027383	(PI.f32)

Samples

335.0ms

256×

invalid

Compiler

Compiled 692 to 69 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-div: 117.0ms (64.1% of total)

ival-mult: 41.0ms (22.5% of total)

ival-add: 14.0ms (7.7% of total)

ival-log: 5.0ms (2.7% of total)

ival-sub: 2.0ms (1.1% of total)

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

exact: 1.0ms (0.5% of total)

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

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

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

series314.0ms (2.6%)

Memory

-35.4MiB live, 55.0MiB allocated

Counts

25 → 348

Calls

Call 1

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

Calls

99 calls:

Time	Variable		Point	Expression
149.0ms	alpha	@	-inf	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
12.0ms	alpha	@	-inf	(log alpha)
6.0ms	alpha	@	inf	(log alpha)
6.0ms	alpha	@	0	(log alpha)
2.0ms	cosTheta	@	inf	(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (+ (* alpha alpha) 1) alpha) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify512.0ms (4.2%)

Memory

47.1MiB live, 329.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 768×	`lower-*.f64`
6 768×	`lower-*.f32`
5 530×	`lower-fma.f64`
5 530×	`lower-fma.f32`
3 678×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	539	10756
1	1731	10190
2	7960	10190
0	8280	9727

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

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))))))))
(/ -1/2 (* (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))))))
(/ -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) 1) (* (PI) (log (pow alpha 2))))
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(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
-1
(- (pow alpha 3) 1)
(- (pow alpha 3) 1)
(- (pow alpha 3) 1)
(pow alpha 3)
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(pow alpha 3)
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(log alpha)
(log alpha)
(log alpha)
(log alpha)
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* cosTheta (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (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) (- (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))
(* -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 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 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)))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))

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

rewrite29.0ms (0.2%)

Memory

-7.2MiB live, 37.7MiB allocated

Rules

60×	`lower-*.f64`
42×	`lift-*.f32`
28×	`lower-+.f64`
22×	`lower-/.f64`
20×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	427
0	140	425

Stop Event

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

Counts

25 → 27

Calls

Call 1

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

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

eval101.0ms (0.8%)

Memory: -21.4MiB live, 80.8MiB allocated
Compiler: Compiled 22 963 to 648 computations (97.2% saved)

prune414.0ms (3.4%)

Memory

-9.0MiB live, 127.6MiB allocated

Pruning

37 alts after pruning (35 fresh and 2 done)

	Pruned	Kept	Total
New	575	17	592
Fresh	7	18	25
Picked	3	2	5
Done	0	0	0
Total	585	37	622

Accuracy

100.0%

Counts

622 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 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))))
	98.3%	(/.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))))
	98.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 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) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (+.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)) -1) (+ (* alpha alpha) -1)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))) (.f32 (+.f32 (fma.f32 alpha alpha #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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) #s(literal 1 binary32))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	97.4%	(/.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 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))) (.f32 (neg.f32 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	97.2%	(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 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))))
▶	98.3%	(/.f32 (.f32 (+.f32 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))))
	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 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	98.7%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
✓	66.9%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	65.1%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	-0.0%	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
✓	94.2%	#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 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	94.3%	#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 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	94.4%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (fma.f32 (.f32 alpha alpha) (fma.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32)) #s(literal -1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	81.9%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	74.4%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	93.8%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (.f32 (+.f32 #s(literal -1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha))))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	65.5%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	66.8%	#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 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	66.8%	#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 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	94.7%	#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)))) #s(approx (/ (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (* (PI) (* (log (* alpha alpha)) (* (+ alpha 1) (+ (* alpha alpha) (- 1 alpha)))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))))
	65.1%	#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)))) #s(approx (/ (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (* (PI) (* (log (* alpha alpha)) (* (+ alpha 1) (+ (* alpha alpha) (- 1 alpha)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
	94.2%	#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)))) #s(approx (/ (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (* (PI) (* (log (* alpha alpha)) (* (+ alpha 1) (+ (* alpha alpha) (- 1 alpha)))))) (.f32 (.f32 alpha alpha) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))))
	94.3%	#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 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32))))))
	94.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	94.8%	#s(approx (/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (-.f32 (fma.f32 alpha alpha alpha) alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))

Compiler

Compiled 1 999 to 1 106 computations (44.7% saved)

simplify11.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))))
cost-diff	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))))
cost-diff	0	(+.f32 alpha #s(literal -1 binary32))
cost-diff	0	(+.f32 alpha #s(literal 1 binary32))
cost-diff	0	(*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 (.f32 (+.f32 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))))
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 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)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
cost-diff	0	(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
cost-diff	0	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32)))
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 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	648
0	101	644

Stop Event

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

Calls

Call 1

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

localize924.0ms (7.6%)

Memory

16.9MiB live, 259.9MiB 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	29.987880231027383	(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	29.987880231027383	(PI.f32)
accuracy	0	(neg.f32 cosTheta)
accuracy	0	(log.f32 alpha)
accuracy	0	#s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32))))
accuracy	29.987880231027383	(PI.f32)
accuracy	0	(neg.f32 cosTheta)
accuracy	0	#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
accuracy	0	#s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))
accuracy	29.987880231027383	(PI.f32)
accuracy	0	(log.f32 alpha)
accuracy	0	#s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0	#s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
accuracy	29.987880231027383	(PI.f32)

Samples

578.0ms

256×

invalid

Compiler

Compiled 573 to 52 computations (90.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 269.0ms

ival-pi: 211.0ms (78.4% of total)

ival-mult: 30.0ms (11.1% of total)

ival-div: 12.0ms (4.5% of total)

ival-add: 8.0ms (3% of total)

ival-log: 5.0ms (1.9% of total)

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

exact: 1.0ms (0.4% of total)

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

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

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

series262.0ms (2.2%)

Memory

-14.1MiB live, 32.5MiB allocated

Counts

25 → 336

Calls

Call 1

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

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

Calls

96 calls:

Time	Variable		Point	Expression
241.0ms	cosTheta	@	0	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	inf	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
0.0ms	alpha	@	0	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
0.0ms	alpha	@	-inf	(* (+ alpha 1) (+ alpha -1))

simplify1.6s (13.4%)

Memory

1.6MiB live, 285.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 232×	`lower-fma.f64`
8 232×	`lower-fma.f32`
5 486×	`lower-*.f64`
5 486×	`lower-*.f32`
2 932×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	305	8282
1	996	8014
2	4161	7627
0	8165	7303

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 332

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

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

rewrite94.0ms (0.8%)

Memory

-18.1MiB live, 47.3MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	355
0	101	351

Stop Event

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

Counts

25 → 26

Calls

Call 1

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

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

eval48.0ms (0.4%)

Memory: 26.9MiB live, 71.2MiB allocated
Compiler: Compiled 17 857 to 379 computations (97.9% saved)

prune109.0ms (0.9%)

Memory

-24.2MiB live, 124.1MiB allocated

Pruning

39 alts after pruning (36 fresh and 3 done)

	Pruned	Kept	Total
New	535	12	547
Fresh	6	24	30
Picked	3	2	5
Done	1	1	2
Total	545	39	584

Accuracy

100.0%

Counts

584 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.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 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 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))))
	98.3%	(/.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))))
	98.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))) (.f32 (+.f32 (fma.f32 alpha alpha #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))))
	97.0%	(/.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 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) #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))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	82.0%	(/.f32 (/.f32 #s(literal 1 binary32) #s(approx (/ 1 (+ (* alpha alpha) -1)) (fma.f32 alpha (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))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha cosTheta cosTheta) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta) #s(literal 1 binary32))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	97.2%	(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (neg.f32 (+.f32 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))))
	97.3%	(/.f32 (.f32 (+.f32 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 #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 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	97.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (PI.f32) #s(literal -2 binary32)) (*.f32 (log.f32 alpha) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))))
	52.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
	98.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (.f32 (neg.f32 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta cosTheta (/.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 alpha alpha))))))))
	98.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)))))
	94.8%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
✓	98.7%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 #s(literal 2 binary32) (fma.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))
	96.9%	(/.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 ( (* (PI) (log (* alpha alpha))) (/ 1 (/ 1 (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)))) (.f32 (.f32 (log.f32 alpha) (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32))) (*.f32 (PI.f32) #s(literal 2 binary32)))))
✓	66.9%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	65.1%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
✓	-0.0%	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
	94.4%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (fma.f32 (.f32 alpha alpha) (fma.f32 alpha (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 1 binary32)) #s(literal -1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	81.9%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (fma.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha) #s(literal -1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	74.4%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	93.8%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (.f32 (+.f32 #s(literal -1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 alpha (.f32 alpha alpha))))) (neg.f32 (pow.f32 alpha #s(literal 5 binary32))))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (*.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	65.5%	#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 #s(approx (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	66.8%	#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 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	66.8%	#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 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	94.7%	#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)))) #s(approx (/ (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (* (PI) (* (log (* alpha alpha)) (* (+ alpha 1) (+ (* alpha alpha) (- 1 alpha)))))) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))))
	65.1%	#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)))) #s(approx (/ (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (* (PI) (* (log (* alpha alpha)) (* (+ alpha 1) (+ (* alpha alpha) (- 1 alpha)))))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
	94.2%	#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)))) #s(approx (/ (* (+ (* alpha alpha) -1) (+ (* alpha (* alpha alpha)) 1)) (* (PI) (* (log (* alpha alpha)) (* (+ alpha 1) (+ (* alpha alpha) (- 1 alpha)))))) (.f32 (.f32 alpha alpha) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))))
	94.3%	#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 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha (fma.f32 alpha alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32))))))
	66.8%	#s(approx (/ (/ 1 (/ 1 (+ (* alpha alpha) -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 (log.f32 alpha) (fma.f32 cosTheta cosTheta #s(literal -1 binary32))))))
	94.8%	#s(approx (/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (-.f32 (fma.f32 alpha alpha alpha) alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))

Compiler

Compiled 3 243 to 870 computations (73.2% saved)

regimes87.0ms (0.7%)

Memory

2.8MiB live, 191.4MiB allocated

Counts

77 → 1

Calls

Call 1

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

Calls

4 calls:

22.0ms	cosTheta
20.0ms	(*.f32 alpha alpha)
20.0ms	(/.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))))
20.0ms	alpha

Results

Accuracy	Segments	Branch
98.7%	1	`cosTheta`
98.7%	1	`alpha`
98.7%	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))))`
98.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes75.0ms (0.6%)

Memory

17.9MiB live, 154.3MiB allocated

Counts

66 → 1

Calls

Call 1

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

Calls

4 calls:

19.0ms	(/.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))))
19.0ms	cosTheta
18.0ms	alpha
17.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
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)`
98.5%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes154.0ms (1.3%)

Memory

-28.4MiB live, 115.1MiB allocated

Counts

49 → 1

Calls

Call 1

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

Calls

4 calls:

80.0ms	alpha
16.0ms	(*.f32 alpha alpha)
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))))
12.0ms	cosTheta

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes48.0ms (0.4%)

Memory

3.6MiB live, 50.9MiB allocated

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

25.0ms	alpha
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	cosTheta
7.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
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)`
98.5%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes64.0ms (0.5%)

Memory

18.3MiB live, 53.5MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

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

Results

Accuracy	Segments	Branch
97.5%	1	`alpha`
97.5%	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))))`
97.5%	1	`(*.f32 alpha alpha)`
97.5%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes46.0ms (0.4%)

Memory

29.5MiB live, 50.9MiB allocated

Counts

15 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

31.0ms	(/.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))))
5.0ms	cosTheta
5.0ms	alpha
5.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
94.8%	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))))`
94.8%	1	`cosTheta`
94.8%	1	`alpha`
94.8%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes20.0ms (0.2%)

Memory

2.8MiB live, 47.0MiB allocated

Counts

12 → 1

Calls

Call 1

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

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 (PI.f32) (log.f32 (*.f32 alpha alpha)))))

Calls

4 calls:

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))))
5.0ms	cosTheta
4.0ms	(*.f32 alpha alpha)
4.0ms	alpha

Results

Accuracy	Segments	Branch
94.8%	1	`cosTheta`
94.8%	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))))`
94.8%	1	`alpha`
94.8%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes18.0ms (0.1%)

Memory

33.3MiB live, 33.3MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

4.0ms	(*.f32 alpha alpha)
4.0ms	(/.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))))
4.0ms	cosTheta
4.0ms	alpha

Results

Accuracy	Segments	Branch
65.1%	1	`cosTheta`
65.1%	1	`alpha`
65.1%	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))))`
65.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes42.0ms (0.3%)

Memory

-8.5MiB live, 26.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

31.0ms	(*.f32 alpha alpha)
4.0ms	(/.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	cosTheta
3.0ms	alpha

Results

Accuracy	Segments	Branch
65.1%	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))))`
65.1%	1	`cosTheta`
65.1%	1	`alpha`
65.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes11.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB 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 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))

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

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

Outputs

(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (*.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (*.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (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	cosTheta
3.0ms	(*.f32 alpha alpha)
2.0ms	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)

simplify77.0ms (0.6%)

Memory

-29.2MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary32`
6×	`sub-neg_binary32`
6×	`+-commutative_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	421
1	121	421
2	126	421
3	132	421

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (12.1%)

Memory

41.1MiB live, 1 220.4MiB allocated

Rules

8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
8 232×	`lower-fma.f64`
8 232×	`lower-fma.f32`
6 768×	`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	197	2350
1	582	2290
2	2231	2197
0	8730	2075
0	539	10756
1	1731	10190
2	7960	10190
0	8280	9727
0	468	10368
1	1562	9952
2	7068	9888
0	8086	9428
0	305	8282
1	996	8014
2	4161	7627
0	8165	7303

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 866 to 343 computations (60.4% saved)

preprocess212.0ms (1.7%)

Memory

-22.2MiB live, 172.7MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 808 to 358 computations (55.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze85.0ms (0.7%)

sample2.1s (17.3%)

explain165.0ms (1.4%)

preprocess314.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify255.0ms (2.1%)

localize45.0ms (0.4%)

series54.0ms (0.4%)

simplify317.0ms (2.6%)

rewrite307.0ms (2.5%)

eval77.0ms (0.6%)

prune173.0ms (1.4%)

simplify12.0ms (0.1%)

localize154.0ms (1.3%)

series48.0ms (0.4%)

simplify255.0ms (2.1%)

rewrite77.0ms (0.6%)

eval378.0ms (3.1%)

prune90.0ms (0.7%)

simplify21.0ms (0.2%)

localize473.0ms (3.9%)

series314.0ms (2.6%)

simplify512.0ms (4.2%)

rewrite29.0ms (0.2%)

eval101.0ms (0.8%)

prune414.0ms (3.4%)

simplify11.0ms (0.1%)

localize924.0ms (7.6%)

series262.0ms (2.2%)

simplify1.6s (13.4%)

rewrite94.0ms (0.8%)

eval48.0ms (0.4%)

prune109.0ms (0.9%)

regimes87.0ms (0.7%)

regimes75.0ms (0.6%)

regimes154.0ms (1.3%)

regimes48.0ms (0.4%)

regimes64.0ms (0.5%)

regimes46.0ms (0.4%)

regimes20.0ms (0.2%)

regimes18.0ms (0.1%)

regimes42.0ms (0.3%)

regimes11.0ms (0.1%)

simplify77.0ms (0.6%)

soundness1.5s (12.1%)

preprocess212.0ms (1.7%)

end0.0ms (0%)

Profiling